0
votes
0answers
30 views

How to plot this function

How to plot this function in WolframAlpha or some other graphing calculator? $f(x) =\left\{\begin{matrix} 1 & -\dfrac{-2\pi}{3} \leq x \leq \dfrac{2\pi}{3}\\ -1 & ...
1
vote
2answers
56 views

Why isn't $f(x)=\sqrt{2-x}$ reflected across the y-axis?

If I try to graph this function, it does not appear to reflect across the y-axis when it comes time to do the reflection. Rather, it is reflected around the point where the function begins on the ...
0
votes
1answer
22 views

Finding the vertical shift of a sinusoidal function

I'm currently studying sinusoids, I've been given a graph with a few key points and have been told to find a cosine function which fits it. When it comes to finding the vertical shift of the graph the ...
0
votes
1answer
56 views

Limit of a function containing square root.

Q. $\lim _{x\to 0}\frac{\left(\sqrt{1-cos2x}\right)}{x}$ We can write this function as $\lim _{x\to 0}\frac{\left(\sqrt{2sin^2x}\right)}{x}$. Algebraically we have ...
1
vote
2answers
58 views

How to find the equation of the graph reflected about a line?

Consider the graph of $y = e^x$ (a) Find the equation of the graph that results from reflecting about the line $y = 4$. (b) Find the equation of the graph that results from reflecting ...
2
votes
1answer
56 views

Function - Main Features?

I understand how to draw this function, but what does it mean by main features? any examples for the question below? Consider the function $f : \mathbb{R} \rightarrow \mathbb{R}$ given by $f(x) = ...
1
vote
2answers
51 views

Why does the graph not show the vertical asymptote?

I have a rational function in which the denominator is equal to zero when $x = -1.4142135$. So: $f(x)=\dfrac{1}{x + 1.4142135}$ Then the vertical asymptote at $x = -1.4142135$ is pretty clear. But ...
0
votes
1answer
21 views

How to determine a general arithmetic sequence formula for two intersecting trig function

I have equations out of two trigonometric functions. For example $\cos(4\alpha$) = -$\sin(5\alpha)$ $\tan(0.5\alpha$) = 2 $\sin(\alpha)$ How can I determine a general arithmetic sequence formula ...
-1
votes
1answer
20 views

Straight lines - point of intersection

Question: Two rays in the first quadrant: $$x +y = |a|$$ $$ax - y = 1$$ intersect each other in the interval $a \in (a_0, \infty)$, the what is the value of $a_0$? I don't even understand where to ...
0
votes
1answer
18 views

Find a function matching this scheme

As I'm building a model, I need a function equals to $+\infty$ in 0, $-\infty$ in R and 0 in $\frac{R}{2}$. So it will looks like this (sorry for this bad drawing I'm at work). It definitely looks ...
3
votes
2answers
91 views

Behaviour of the function $\ln(1+ x^2)$

Thus function has derivative equal to: $\frac{2x}{1+x^2}$. This indicates that it will flatten out while approaching infinity, ie, should have an asymptote. Yet, the function does not have any real ...
2
votes
1answer
95 views

How to solve $\tan x=x^2$ in radians?

How to solve $\tan x=x^2$ with $x \in [0, 2\pi]$? I try with trigonometry and many ways but the numerical solutions seems to be difficult.
1
vote
4answers
53 views

How to determine the periods of a periodic function?

I am aware of the other similar questions but was not able to figure out what I want to know from those question thus posting it here. Given a periodic function $f(x)=sin(x)$, Why is the period ...
2
votes
2answers
56 views

If a one-to-one function's inverse is the same what must be true of the graph of f?

As a followup to this question. I'm trying to determine what must be true of the graph of $f$ in these cases. I've examined the two functions $f(x)= x$ and $f(x)= \frac{1}{x}$ and I'm not seeing any ...
5
votes
2answers
585 views

Do odd functions pass through the origin?

An odd function is symmetrical in the 1st and 3rd quadrants. Does this means that it always passes through the origin?
1
vote
1answer
93 views

How to graph $y=f(x^2)=\sin(x^2)$?

How to graph $y=f(x^2)=\sin(x^2)$? I have substituted as follows: $$\begin{cases} y=f(a)=\sin a\\ a=x^2\end{cases}.$$ Then if I graph this with the coordinate axes $y$ and $a$ I get the ordinary ...
0
votes
0answers
87 views

Function's graph sketch

$f(x) = x+9$ $g(x) = 2x-3$ I need to draw the sketch of $\min(f,g)$ and $\max(f,g)$. I tried: http://sketchtoy.com/62375984 The yellow is the min and the blue is max. The lines should be ...
1
vote
2answers
56 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: $-4, -3, -2, -1, 0, 1, 2, 3, 4$?
2
votes
2answers
31 views

Establish the absolute maximum of a function

We have this function:$$f(x)=\begin{cases} \sin(x) \cdot\ln(\sin2x), & \mbox{if }0<x<\pi/2 \\ 0, & \mbox{if }x=0,\mbox{or }x=\pi/2 \end{cases}$$ So, how to prove that it decreases and ...
0
votes
0answers
14 views

need for a function suggestion to fit data

I have calculated some data which looks like the figure below, I was used to use spline to fit the data but I noticed that the data form looks rather similar to zeta and 11/r functions so I was ...
-1
votes
1answer
44 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
24 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!
0
votes
1answer
45 views

How to identify the function of a graph?

I am trying to identify the function of a graph in order to create a dataset for it. Dataset as in several x/y-values that will lead Excel/PowerPoint to create a graph looking just like the drawing: ...
4
votes
5answers
245 views

A simple function equation

I come from a programming background and I can’t find a simple math function. The request might seem strange, but I needed it a graphical context to alter some points locations: I need a function ...
2
votes
3answers
98 views

Find the coefficients $a, b, c$ and $d$ so that the curve shown in the accompanying figure is the graph of the equation.

Find the coefficients $a, b, c$ and $d$ so that the curve shown in the accompanying figure is the graph of the equation $y = ax^3 + bx^2 + cx + d$. I have no clue how to solve this. This looks like ...
14
votes
12answers
2k views

How to explain the perpendicularity of two lines to a High School student?

Today I was teaching my friend from High School about linear functions. One of the exercises we had to do was finding equations of perpendicular and parallel lines. Explaining parallel equations was ...
1
vote
3answers
61 views

Why rotating a function around line $y=x$ gives an inverse of this function?

So I'm trying to read through a book on calculus on my own and there is a statement that if we have a graph of some function $y=f(x)$ and this is an injective function, then rotating it around the ...
0
votes
0answers
30 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
1answer
24 views

Finding b coefficient by looking at shape of parabolas

I was given the graphs: I was told to say whether the a, b and c coefficients in y=ax^2+bx+c were positive or negative for each graph. The a and c coefficients can be found just by looking at the ...
0
votes
0answers
31 views

Identify functions by their graphics

I know it is inprecise, but can anybody suggest analytic functions that fit the following graphics? Here the blue curve is $(\sec x)^2$, need to identify red and yellow. Here the blue curve is ...
0
votes
2answers
29 views

$y = xe^{−1/|x|}$ for $−∞ < x < ∞$

(a) Let $f(x) = x − xe^{−1/x}, x > 0$. Show that f(x) is an increasing function on $(0,∞),$ and $\lim_{x→∞} f(x) = 1$. (b) Using part (a) and calculus, sketch the graphs of $y = x−1, y = x, y = x ...
0
votes
2answers
28 views

Find the graph of the derivative

The graph of a function $f$ defined on $(0,2)$ with the property $\lim_{x\to 0^+}f(x)=\lim_{x\to 2^-}f(x)=\infty$ is as follows:
2
votes
1answer
25 views

Predict the nature of the curve

$$f(x)=\int_0^{\sqrt{x}}e^{u^2\over x}du$$ Hence predict the graph of $f(x)$:
0
votes
1answer
63 views

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.
0
votes
1answer
161 views

How do you minimize “hinge-loss”?

A lot of material on the web regarding Loss functions talk about "minimizing the Hinge Loss". However, nobody actually explains it, or at least gives some example. The best material I found is here ...
0
votes
0answers
6 views

Steps in Anlaysing Surface Plot

I have two vectors ${\bf x}$, ${\bf y}$ such that $0 \leq x_i, y_j \leq 1$ and a third vector ${\bf z}$ where $z_i \in \{0,1\}$. Each row of the vectors represents an 'observation' and I am trying to ...
0
votes
3answers
67 views

Find the locus of points

Find the locus of points, the distance between them and the point $(2,1)$ is equal to the distance between them and the straight line $4x = 3y$ I know that it is the definition of a parabola But I ...
0
votes
0answers
19 views

Interpreting functions of graphs

The question asked which of the following is false. I narrowed it down to two, and the correct answer is E with it doesn't cross the x-axis at all. D. f(x) * g(x) intersect the x-axis three times E. ...
0
votes
1answer
41 views

Problem with graphing a function.

To my understanding, function $f(x)=\frac{1+x}{1+x^3}$ should not be defined with $x=-1$ since: $f(-1)=\frac{1+(-1)}{1+(-1)^3}=\frac{1+(-1)}{1+(-1)}=\frac{0}{0}$ However, Google's plot drawer and ...
1
vote
0answers
41 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
2answers
73 views

How do you shift a sigmoidal curve to the right?

How do you shift the function $1$ $/ ( 1 + e ^ {-x} )$ to the right without altering the shape of the curve?
0
votes
2answers
36 views

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 ...
0
votes
1answer
22 views

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 ...
0
votes
1answer
12 views

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?
1
vote
3answers
47 views

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 ...
1
vote
2answers
25 views

Symmetry of product of symmetric functions

Let's say we have three functions, $f(x), g(x) \text{ and }h(x)=f(x)\cdot g(x)$, all of which are defined for $x \in [-1,1]$. If $f(x) \text{ and }g(x)$ are symmetric around the y-axis, will $h(x)$ ...
0
votes
1answer
44 views

Partial derivatives and functions equal to 0

If I have the function (family of curves) $$F(x,y,p)=(px)^2+p=0$$ I am under the impression that $$\frac{\partial F(x,y,p)}{\partial p}=2px^2+1$$ Is not always equal to $0$. Please could you ...
0
votes
1answer
31 views

how to define a function which returns a multiset

Given graph $G(V,E)$, how can I formally define function $f\prime$ which takes a node $v \in V$ and returns a multiset?
2
votes
1answer
147 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
0answers
28 views

Function plotting

I have a function $f(x)=\binom{N}{K} \ln(1-F(x)), x \geq 0$, where $F(x)$ is a cumulative distribution function. Then, $\ln(1-F(x))$ is negative for various values of $x$ as $F(x) \geq 0$. Also, ...