# Tagged Questions

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### Which set of points are defined by the relation $x/|x|=y/|y|$?

Which set of points are defined by the relation $x/|x|=y/|y|$? I think the answer is a straight line bisecting the first and third quadrants through the origin ( ie the line x=y). However wolfram ...
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### sketching the graph

how to sketch the graph $|x+y|= m$, when $m$ is some real number? I personally can not see any efficient or known method to do so...
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### Graphing rational functions

Graph the rational function $f(x)=\frac{-4}{-x-2}$ Please help me figure out how to start this problem.
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### Graph all vertical and horizontal asymptotes [closed]

Graph all vertical and horizontal asymptotes of the function $$f(x)=\frac{-10x-11}{-4x-2}.$$ Please help me figure out how to start this problem.
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### Graphing polynomials

Sketch a graph of the polynomial $P(x)=(x-2)^2(x+1)^3$. You must plot and label the x and y intercepts and these should be the only points you plot. How do I sketch the graph of a polynomial?
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### Straight Line Graph questions

Sorry if the questions is too long My question: how do i find the gradient of the following picture below? I know this formula is required Y= y2-y1/x2-x1 but how do i find out equation of line 2 ...
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### Help with linear function, I think

In Argentine, the cost of kW/h is $4,5$ cents and in Latin America, $16$ ctvs (average). a) In how many months would you update the cost to reach $16$ cents kW/h, applying a linear $20\%$ increment ...
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### Sketching the graph of $y =\ln(4-x)$

$y = \ln(4 - x)$ This graph has two operations applied to the $\ln x$ graph - a reflection and a translation. If you reflect the graph in the $y$-axis first, and then shift the graph 4 units to ...
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### What is the number of x-intercepts in this graph of sine?

The function : $y=3-4\sin(2\pi x-3\pi)$ .. how many $x$-intercepts over the interval $[0,2]$? I am confused if they're 3 or 5 because there are 3 $x$-intercepts that are really intercepting ...
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### Graph this function: F(x)=$-2^{|x|+1}$.

Graph this function: F(x)=$-2^{|x|+1}$. when I graph this function and go to check by a graphing calculator I find that I am wrong ! even though I do the horizontal translation So, what's wrong? ...
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### How to find last pt of triangle

How to find last pt of triangle. I got (1,7) and (0.5, 4). The equations are y = 3|2x − 1| + 4 and y = −|x − 4| + 10
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### Sketching the spectrum of a signal

The figure below shows Fourier spectrum of a signal $g(t)$ Sketch the spectrum of the signal $2g(t)\cos^2(100\pi t)$. Show value in sketch.
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### Graphing a Circle that doesn't have two of each variable

Graph the circle: $$x^2+y^2-2x-15=0$$ I know how to approach this problem if there were two $y$ and $x$ variables. But there is only one $y$ variable. How would I approach this?
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### Curve Sketching - transforming f(x) to f(a-x)

In class I learnt that to sketch $y=f(a-x)$ given a graph of $y=f(x)$, you reflect the given graph about the line $x=a/2$ (this was proven to us). And then the teacher said that something we ...
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### Finding the Asymptote / Root of a reciprocal function

$$y = \frac{3}{8x - 3}$$ The y-intercept is $-1$ and the vertical asymptote is $x = \frac{3}{8}$ but what would be the horizontal asymptote and the x-intercept in this case? I am asking this as the ...
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### Functions (Finding Inverse)

$f(x) = x^2 + 2x$ , domain ${x ≥ 1}$ Question: find the inverse The inverse is $f(x) = 1 + \sqrt(1+x)$ (taking the positive square root only) As $f^{-1}(5) = 2$ and as 2 is an element from the ...
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### Functions inverse + domain

Question part a): !([http://imgur.com/sKJbFKu]) Answer: !http://imgur.com/jRfeXkW Can anyone explain why the inverse must be the negative square root?
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### Functions definition + question

Am I correct in saying that for Functions, the below is the correct definition: For each value of x in the domain there is only one value of y in the range. Hence, the picture below means that it is ...
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### how do i write an equation in standard form by completing the square for $x^2 -9y^2-4x-18y=14$

I'm really having trouble with completeing squares i can solve for circles and ellipses but i can't seem to understand hyperbolas or parabolas, help would be deeply appreciated.
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### A sequence made from a function under a certain rule.

I have been working on this question . My attemt at this question so far: $(a)$ From the diagrams I figured out the pattern to be as follows $x_{0},f(x_{0}),f(f(x_{0})),....$ wherin $x_{0}=x_{0}$ ...
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### Rewrite $f(x) = 3 \sin (\pi x) + 3\sqrt{3} \cos (\pi x)$ in the form $f(x) = A \sin (Kx+D)$

I got a question like that said "Rewrite $f(x) = 3 \sin (\pi x) + 3\sqrt{3} \cos (\pi x)$ in the form $f(x) = A \sin (Kx+D)$". I'm inclined to think that since the periods are the same ($2$), that ...
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### Finding intersection points of 2 functions. My method is incomplete.

These are the 2 functions : $y = x^{4}-2x^{2}+1$ $y = 1-x^{2}$ Here's how I solved It : $x^{4}-2x^{2}+1 = 1-x^{2}$ $x^{4}-x^{2} = 0$ $x^2(x^2-1)=0$ $x^2-1=0$ $x=\pm \sqrt{1}$ Value of $y$ when ...
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### Write an equation that approximates this relationship. Y = Seconds of daylight in day, X = a range of days

Disclaimer: This is a project for a math class. (who does math for fun anyways? Jk I actually enjoy math when I understand it, and not so much when I feel lost, but I digress ) The problem roughly ...
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### The graph of the function is $g(x)=x^3-2x^2+x+1$ and the tangent to the curve is at $x=2$?

a) Find the equation of the tangent to the curve at $x=2$ HELP and then b) Determine the angle that this tangent makes with the positive direction of the $x$-axis Please help I really need to ...
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### Calculus: tangents and limits

For 1), I know the graph has a tangent but I don't know how to explain. For 2), is the answer 0? Would anyone mind giving me the steps? For 3) and 4), I really have no idea.
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your classmate juan missed the lesson on graphing linear equations using slope-intercept form. you attend the class and what to help juan understand the material he missed. assume juan knows how ...
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### Frequency response of Continous-time system

Not sure where to start on this one: $$H(s)={(s-j\omega_0)(s+j\omega_0)\over(s+\omega_0\cos\theta+j\omega_0\sin\theta)\left(s+\omega_0\cos\theta-j\omega_0\sin\theta\right)}$$ Sketch the frequency ...
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### Homework - Square Root Functions with Exponents

I am doing square root graphs in school and on the homework, one problem was $$f(x) = \sqrt{x^2-25}$$ I know that there is a horizontal translation of positive 25, but how would I graph the $x^2$ ...
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### In the graph [(3x+12)(x-2)]/[(x-1)(x+5)], the graph at one point crosses the horizontal asypmtote. How come?

I did the graph on my calculator and saw that it crosses the horizontal asypmtote right in middle. But, how is that possible? (I don't know how to insert graphs just yet ... )
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### Multiplying a function by negative numbers [closed]

I have a question on a problem I saw. You are given a picture of a graph where there is a semi circle with a radius of $1$ point and the circumference of the circle lies on $(0,-2)$ and $(2,-2)$. ...
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### Determining the positioning of rational functions without plotting points

When graphing rational functions, how do I determine the orientation of a rational function around the asymptotes without plotting points? For example, is it possible to determine which one of these ...
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### Orthogonal problem

Show that $$xy=a, a≠0$$ is orthogonal to every curve $$x^2-y^2=b, b≠0$$ So I know, that the derivative at every intersecting curve is perpendicular. I don't know how to continue this problem because ...
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### Finding the area of a region?

I sketched out the graph to get this figure but I can't seem to find the area of the shaded region... would one Y = 4 and the other Y = 8? I, in all honesty, am so flabbergasted with this question, ...
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### Find the area of the shaded region?

So the question is listed below as a picture, I realize I have to subtract the min and max after inputting them into the equation. So far I think it would be integral x going from 0 and going to 11/2? ...
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### Graph Transformation Question

I get that because x^2 will be negative the answer will be one of the following a, b, or e. But I don't understand why the answer is a??
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### Can you help me with this question x - y ≥ 2

Good evening, I have a problem doing this question: Graph the solution set of X - y ≥ 2. Where do I start from? and how to do these types of questions?
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### How do you go about creating these graphs out of this problem

I'm trying to solve a list of math exercises and got stuck on this one. I have no idea of how to go about solving it. It asks to build 3 graphs, but if someone could explain just one of them I should ...
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### Giving the domain and range of an equation. *not same problem as previously asked question* [closed]

I need help with a problem. *not same as a question i previously asked, it has a different question!* noting because someone downvoted... Given the function f(x) has a domain D: {-3,-1,0,2} and a ...
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### Need help with finding domains, intercepts, max/min of function

Here is a picture for clarification of the question: So far, I have gotten this: the root is all non-negative numbers; x is greater than or equal to 0. In order to find the asymptotes I set the ...
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### Use a graph to estimate the time at which the number was increasing most rapidly

For the period from 2000 to 2008, the percentage of households in a certain country with at least one DVD player has been modeled by the function $f(t) = \frac{87.5}{1 + 17.1e^{−0.91t}}$ where the ...
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### Finding range of functions

I was wondering if there is a sure fire process of finding the ranges of functions without plotting them on a graph? At the moment (only for quadratics) I find the vertex of the graph through ...
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### How to draw a set $\{(x,y): y^2 \leq x^2\}$

I want to draw a set $\{(x,y): y^2 \leq x^2\}$. I know what the result should look like (the blue region): But I don't really see why is that so. I have $$y^2 \leq x^2$$ I am dividing the ...
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### sketching the graph of functions

Good morning! How to draw the graph of the following function and discuss the increasing and decreasing intervals of y. $y =$x$+ \sqrt[]{x^2}$ Also, I would like to know free online graphing ...
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### What is the Y-intercept?

In class, my math teacher was teaching us how to draw functions on a coordinate plane, and he mentioned something about the Y-Intercept being an important step in creating/solving a function. But, ...
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### How many solutions does $\tan(\frac{1}{x}) = 0$ have on the interval $-1 \leq x \leq 1$?

How many solutions does $\tan(\frac{1}{x}) = 0$ have on the interval $-1 \leq x \leq 1$? I do not know how to get the coefficient of $x$ here. I put this into a graphing calculator and it gave me a ...
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### Solving Linear Systems of Differential Equations - Phase Portraits

I'm working on trying to find the phase portrait for a differential equations such that $$A = \begin{matrix} a_1 & a_2 \\ 0 & a_3 \end{matrix}$$ so that x_1'(t) = a_1x_1+a_2x_2 \text { and ...
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### A graphical approach to composition of functions and iteration problem.

I have a problem with the following exercise: As we saw in this section, the iteration process can be carried out either algebraically or graphically. Composition of functions can also be ...
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### growth equation with time lags?

To understand logistic growth, (say for example population growth) we employ a Verhulst-Pearl logistic equation and introduce a time lag to account for the fact that the system under study takes some ...
I'm trying to calculate the slant asymptotes of the function $\sqrt{x^2+2x+2}$. I've found out that the gradients of the asymptotes are 1 for $x\rightarrow+\infty$ and -1 for $x\rightarrow-\infty$. ...