1
vote
2answers
40 views

Graph a function

I have a question, I have a function: $$f(x) = \frac{-x^2-10x}{2}$$ I'm really confused how to replace the x. So, what would be the points in $y$ if $x$ were: $-4, -3, -2, -1, 0, 1, 2, 3, 4$?
0
votes
3answers
50 views

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...
0
votes
1answer
23 views

How to draw the graph of $|x|+|y|=1+x$ and $y+|y|=x+|x|$.

There is this question that asks to draw the graph of $|x|+|y|=1+x$ and $y+|y|=x+|x|$. I know how to draw the graph of $y=\ldots$ using elementary techniques of translating, dilating, etc. But this ...
0
votes
2answers
37 views

Parametric Equations

$x=3\sin^3t$ $y=3\cos^3t$ How would I even begin to work out this one? I'm supposed to graph it, but I have no clue what how to even start it.
-1
votes
1answer
37 views

Why does $f(x) = x \cos 4x$ lie below the $x$-axis in ther interval $[\pi/4, \pi/3]$?

How can I explain why function $f(x)$ lies below the $x$-axis in the interval $\left[\dfrac{\pi} 4, \dfrac{\pi} 3\right]$ where $f(x) = x \cos 4x$?
0
votes
1answer
21 views

Graphing functions

I am having problems understanding how to graph the product $fg$ when $f(x) = x$ and $g(x) = |x|$. Any help would be much appreciated!
-1
votes
3answers
34 views

Graphing rational functions

Graph the rational function $f(x)=\frac{-4}{-x-2}$ Please help me figure out how to start this problem.
-4
votes
1answer
47 views

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.
0
votes
1answer
16 views

Types of graphs for this

How many ways could this be graphed, in a way such that it shows that the degree or slope of a surface affects the average speed. I think T1, t2 etc means at second 1, second 2. This was done using a ...
0
votes
5answers
69 views

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?
-2
votes
1answer
40 views

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 ...
0
votes
1answer
46 views

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 ...
2
votes
3answers
37 views

Having trouble graphing circles and semi circles

I was asked to graph $y = \sqrt{1-x^2}$. How do I do that? I tried to do a table of values but that did not turn out correct Is their a trick to graphing circles, semi circles, hyperbolas etc
0
votes
0answers
28 views

Graphing inequalities, elementary geometry (Highschool level)

I am going through some past papers, and one of the few questions I need help with are: For the second one, relating to plotting the square root of 4 - $x^2$, I did a table of values starting ...
0
votes
4answers
69 views

Multiple choice question on rates of change (or so I thought)

If I were to find the resistance of the component (see image below), I would either find the equation of the curve and use differentiation or I'd draw a tangent at $V_2$ and then find the reciprocal ...
0
votes
3answers
64 views

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? ...
0
votes
1answer
36 views

What's a fast way to sketch $y=\sin (5x) + \frac{3}{10}x \sin (5x)$?

What's a fast way to sketch $y= \sin (5x) + \frac{3}{10}x \sin (5x)$ ? I had this question as part of a recent test paper and I had to sketch it for the range $0 \leq x \leq \pi$ . It was for only 2 ...
0
votes
1answer
15 views

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
0
votes
1answer
28 views

Drawing a graph of $x\cos\left(\frac 1x\right)$

I have been given a question which asks to draw the graph of $x\cos\left(\frac 1x\right)$ without a calculator. However, I'm unsure as to how to do this. It may involve differentiation as that was the ...
0
votes
1answer
58 views

Drawing polar graphs when given theta in terms of the radius

I know how to plot when it is like $r=10 \cdot \sin(2\theta)$. But how to do that when the condition is like: $\theta =2 \pi \cdot \sin(r)$?
1
vote
0answers
35 views

How to approach sketching sine and cosine graphs with transformations

Any tips or suggestions in sketching these graphs quickly, and in ONE go? In exams, I don't want to spend ages re-drawing the original sine/cosine graph, one by one, following each new ...
0
votes
1answer
27 views

Choosing values for octave/decade scale

I am developing a frequency response simulator for linear circuits which should be able to plot graphs of Voltage x Frequency with the latest varying linearly, in octaves or in decades. The only ...
0
votes
4answers
47 views

Equation of a line

I've been practising some past previous exam question and came across this: How would you find the equation of the line with y-intercept? -$\frac{3}{4}$ and slope -$\frac{1}{2}$?
2
votes
1answer
92 views

Sketch the graph of the polynomial function: $S(x) = \frac{1}{2} (x-1)^3 +4.$

The question is: Sketch the graph of the the function by transforming the graph of an appropriate function of the form $y = x^n$. Indicate all x and y intercepts on the graph. I am really trying ...
0
votes
2answers
57 views

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.
1
vote
1answer
24 views

Sketching Logs with Quadratic Terms

$\log(x^2+1) = y$ asymptote at $x^2+1 > 0$ and so there is no asymptote $x$ and $y$ intercept at $(0,0)$ How do you know that the function goes both directions, and has a dip in the middle? ...
1
vote
1answer
52 views

How does one create a step function?

Is there a general form for the equation of a step function? For example, if I wanted to find the equation of this particular step function: How would I go about doing so? At first I was thinking of ...
2
votes
1answer
37 views

How can I write a formula for this linear segments graph?

I have the following data: 60 items = $1 3,600 items = $20 86,400 items = $260 604,800 items = $1,000 Which I have used to make a line graph like so: Is there a way I can ...
0
votes
2answers
39 views

Constant graphs

I need to graph $1 \over d^2$ with average light intensity, where $d$ is $5,10,15,20,25,30$ (i.e. squared would be equal to $1\over25$$1\over100$$1\over225$$1\over400$$1\over625$$1\over900$). The ...
1
vote
1answer
95 views

(Basic High School Mathematics) Graphing the inverse square law

I did an experiment measuring the intensity of light in relation to the distance away from a source. How would I graph the avg intensity over 1/distance squared? Note that T1 = trial 1 etc.. It's ...
1
vote
1answer
23 views

function inversion and the horizontal shift

I am currently doing inverse functions and graphing radical equations of the form $y=a\sqrt{x-h}+k$ with my algebra class and one of my students asked me the following question. "Why is it that we ...
2
votes
5answers
104 views

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 ...
1
vote
1answer
48 views

Inverse Function + Reflection In Y-Axis

Not getting any of the answers in MC. Is the answer wrong, or have I done something wrong?
1
vote
2answers
70 views

Cubic Transformations - Graph shown is best represented by the equation:

The answer is out of B or D: $f(x) = -(x-a)^3 + b$ because turning point at $(0,0)$ is now $(a,b)$ OR $f(x+a)^3$ because "$a$" is implied as negative... $(0,0)$ is now $(-a,b)$ The textbook ...
1
vote
4answers
78 views

Quadratics, transformations, and formulas

Two-part question. Feel free to answer just one part, or both (write which letter part you are answering) a) If the quadratic function $g(x)=a(x-h)^2+ k$ does not touch the $x$-axis, what can be ...
0
votes
0answers
26 views

Graphs of Rational Functions of higher degree

A rational function $f(x)=\frac{kx^n+lx^{n−1}+⋯}{jx^m+ix^{m−1}+⋯}$'s asymptotes are as follows: If $n<m$, then $f(x)$ will approach the line $y=0$ as $x \to \infty$ If $n=m$, then $f(x)$ will ...
0
votes
1answer
27 views

Sin Cos Worded Problem

Stuck at part B. When I directly substitute (3x) for (x) and let f(x)=8/9(root 6) I get the correct answer which is pi/36. But arent you supposed to let 3x=z and then sub (z/3) for x into the ...
2
votes
1answer
55 views

Finding Asymptotes

I'm stuck at understanding why +c is the horizontal asymptote. Can someone please explain this? I get that the vertical asymptote is relating to (x+b), because the denominator cannot=0. But why does ...
0
votes
1answer
57 views

Graphs of functions with fractional powers: $x^{p/q}$

How does changing the value of $\dfrac{p}{q}$ affect the drawing of the graph (domain/range/shape, etc.) How do you calculate asymptotes? Below is a question dealing with this type of function. ...
3
votes
3answers
67 views

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 ...
25
votes
2answers
5k views

Cannabis Equation

How can an equation for the following curve be derived? $$r=(1+0.9 \cos(8 \theta)) (1+0.1 \cos(24 \theta)) (0.9+0.1 \cos(200 \theta)) (1+\sin(\theta))$$ (From WolframAlpha)
2
votes
2answers
51 views

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??
0
votes
2answers
54 views

How do I graph this inequality?

$$y\le x\le \sqrt{1-y^2}$$ Graph: http://www.wolframalpha.com/input/?i=y%3C%3Dx%3C%3Dsqrt%281-y%5E2%29 How would I approach this problem? I graphed $0\le x\le \sqrt{1-y^2}$ easily, but this one is ...
5
votes
2answers
91 views

$P(P(\cdots(P(x))))$ and its integer solutions

Problem: Suppose that $P(x)$ is a polynomial with degree at least $2$ and integer coefficients. Let $Q(x)$ have the form $$ Q(x) = P(P(P(\cdots P(x) \cdots))) $$ for some finite number of nested $P$s. ...
2
votes
0answers
58 views

Should a “good” equation divide the plane?

At the question Is there any equation for triangle? (MSE) the answer given by Henning Makholm received the most upvotes. Therefore let's define the following triangle function $H$ with (a,b,c) the ...
1
vote
0answers
14 views

How an I create a model population?

I need to crate a model population for my Math fair and this is what I have. I need some help with it -I want to find out the size of a population by using a natural exponential function -When I ...
0
votes
0answers
34 views

$\exp(1i * 2 * \pi * (1:K) / K)$ to create clockwise format.

I was reading the documentation of R about text. here in the example : ...
1
vote
1answer
36 views

Plot implicit equation

I'm working with a frequency-response curve of a nonlinear oscillator and came across the following equation (Kovacic & Brennan 2011, p. 179): $$ A^2 = \frac{f^2}{4 \xi^2 \omega^2 + (\omega^2 - ...
0
votes
1answer
56 views

What is the vertex of this parabola and it's min value?

Th equation of the parabola is $$2\left(x+\dfrac34\right)^2−\dfrac{25}8$$ What is the vertex and the min value? and do I just plug $x$ values into the equation to get the points on the graph?
1
vote
1answer
54 views

How do I get the equation for this parabola in standard form?

How do I get the equation for this parabola in standard form? $ y = f(x)= 2x^2+3x-2$