Free Printable Ch 3 - Graphs and equations

1.

What is the interval notation for the given number line?

a)

$\left(2,\ 12\right]$

b)

$\left(3,\ 12\right]$

c)

$\left[3,\ 12\right)$

d)

$\left[3,\ 12\right]$

e)

$\left(2,\ 12\right)$

2.

Given $f\left(x\right)=1-3x^2$ and $g\left(x\right)=3x$ , what is $f\ o\ g\left(-2\right)$ ?

a)

–6

b)

–33

c)

–107

d)

–216

e)

33

3.

What is the solution to the inequation $-4<-2x+1\le5$ ?

a)

$-2\le x<\frac{3}{2}$

b)

$-\frac{3}{2}<x\le2$

c)

$2<x\le\frac{5}{2}$

d)

$-2\le x<\frac{5}{2}$

e)

$-2<x\le\frac{5}{2}$

4.

Which of the following graphs corresponds to $y=x\left(2-x\right)\left(x+1\right)$ ?

a)

b)

c)

d)

5.

What are the vertical and horizontal asymptotes of $y=\frac{6x}{\left(x-2\right)\left(1+x\right)}$ ?

a)

$x=-2$

$x=1$

$y=6$

b)

$x=2$

$x=-1$

$y=0$

c)

$x=-2$

$x=-1$

$y=0$

d)

$x=2$

$x=-1$

$y=6$

e)

$x=-2$

$x=1$

$y=0$

6.

What is the solution of $\left|3x-1\right|=4$ ?

a)

$x=-1,\ x=\frac{5}{3}$

b)

$x=1,\ x=-\frac{5}{3}$

c)

$x=-1,\ x=-\frac{5}{3}$

d)

$x=1,\ x=\frac{5}{3}$

7.

Which formula corresponds to the given diagram?

a)

$y=\left|x-3\right|+1$

b)

$y=\left|x-3\right|-1$

c)

$y=\left|x+3\right|-1$

d)

$y=\left|x+4\right|-2$

e)

$y=\left|4-x\right|-2$

8.

Which of the following sketches correspond to $y<-\frac{x}{2}$ and $y\le2x+3$ ?

a)

b)

c)

d)

9.

Which of the following describes a sine graph with an amplitude of 3 and period of $\frac{\pi}{2}$ ?

a)

$y=9\sin2x$

b)

$y=9\sin\frac{x}{4}$

c)

$y=3\sin\frac{x}{2}$

d)

$y=3\sin4x$

e)

$y=3\sin\frac{x}{4}$

10.

What is the sequence of transformations that will transform $y=\cos x$ to $y=\cos\left(2\left(x+\frac{\pi}{2}\right)\right)+2$ ?

a)

Halve the period, shift horizontally to the right by 𝜋 units, shift vertically downwards by 2 units.

b)

Double the period, shift horizontally to the left 𝜋 units, shift vertically upwards by 2 units.

c)

Double the period, shift horizontally to the right $\frac{\pi}{2}$ units, shift vertically downwards by 2 units.

d)

Halve the period, shift horizontally to the left $\frac{\pi}{2}$ units, shift vertically upwards by 2 units.

e)

Halve the period, shift horizontally to the right $\frac{\pi}{2}$ units, shift vertically upwards by 2 units.

11.

The graph of $y=f\left(x\right)$ is shown.

Which of the following could be the equation of this graph?

a)

$y=\left(1-x\right)\left(2+x\right)^3$

b)

$y=\left(x+1\right)\left(x-2\right)^3$

c)

$y=\left(x+1\right)\left(2-x\right)^3$

d)

$y=\left(1-x\right)\left(2+x\right)^3$

e)

$y=\left(x-1\right)\left(x-2\right)^3$

12.

a)

A

b)

B

c)

C

d)

D

e)

none of these

13.

Which of the following could represent the graph of $y=-x^2+bx+1$ , where $b>0$ ?

a)

b)

c)

d)

14.

Which interval gives the range of the function $y=5+2\cos3x$ ?

a)

$\left[2,\ 8\right]$

b)

$\left[3,\ 7\right]$

c)

$\left[4,\ 6\right]$

d)

$\left[5,\ 9\right]$

e)

$\left[-1,\ 11\right]$

15.

What values of $x$ satisfy $4-3x\le12\ ?$

a)

$x\le-\frac{16}{3}$

b)

$x\ge-\frac{16}{3}$

c)

$x\le-\frac{8}{3}$

d)

$x\ge-\frac{8}{3}$

e)

$x\le\frac{8}{3}$

16.

The diagram shows part of the graph of $y=a\sin\left(bx\right)+4\ .$

WWhat are the values of a and b?

a)

$a=3$

$b=\frac{1}{2}$

b)

$a=3$

$b=2$

c)

$a=\frac{3}{2}$

$b=\frac{1}{2}$

d)

$a=\frac{3}{2}$

$b=2$

e)

$a=4$

$b=\frac{1}{2}$

17.

What is the x intercept of the line $x+3y+6=0\ ?$

a)

$\left(-6,\ 0\right)$

b)

$\left(6,\ 0\right)$

c)

$\left(0,\ -2\right)$

d)

$\left(0,\ 2\right)$

e)

$\left(0,\ -6\right)$

18.

What is the gradient of the line $2x+3y+4=0\ ?$

a)

$-\frac{2}{3}$

b)

$\frac{2}{3}$

c)

$-\frac{3}{2}$

d)

$\frac{3}{2}$

19.

The region enclosed by $y=4-x,\ y=x$ and $y=2x+1$ is shaded in the given diagram.

Which of the following defines the shaded region?

a)

$y\le2x+1$

$y\le4-x$

$y\ge x$

b)

$y\ge2x+1$

$y\le4-x$

$y\ge x$

c)

$y\le2x+1$

$y\ge4-x$

$y\ge x$

d)

$y\ge2x+1$

$y\ge4-x$

$y\ge x$

e)

$y\le2x+1$

$y\le4-x$

$y\le x$

20.

Which diagram best shows the graph of the parabola $y=3-\left(x-2\right)^2\ ?$

a)

b)

c)

d)

21.

Which diagram shows the graph of an odd function?

a)

b)

c)

d)

22.

What is the period of the function $f\left(x\right)=\tan\left(3x\right)\ ?$

a)

$\frac{\pi}{3}$

b)

$\frac{2\pi}{3}$

c)

$3\pi$

d)

$6\pi$

e)

$\frac{3\pi}{2}$

23.

How many solutions does the equation $\left|\cos\left(2x\right)\right|=1$ have for $\left[0,\ 2\pi\right]\ ?$

a)

1

b)

2

c)

3

d)

4

e)

5

24.

How many solutions does the equation $\left|\cos\left(2x\right)\right|=1$ have for $\left(0,\ 2\pi\right]\ ?$

a)

1

b)

2

c)

3

d)

4

e)

5

25.

How many solutions does the equation $\left|\cos\left(2x\right)\right|=1$ have for $\left(0,\ 2\pi\right)\ ?$

a)

1

b)

2

c)

3

d)

4

e)

5

26.

The function $y=\log_{10}x$ is transformed to $y=3\log_{10}\left[2\left(x+5\right)\right]-4$ using only four steps.

Which of the following is not one of the correct steps to transform $y=\log_{10}x$ to the new graph?

a)

Translate down by 4 units

b)

Translate to the left by 5 units

c)

Vertical dilation by a factor of 3

d)

Horizontal dilation by a factor of 2

27.

What is the domain of the function $f\left(x\right)=\ln\left(3-x\right)+\sqrt[]{5x-4}$ ?

a)

$x\in\left(\frac{4}{5},\ 3\right)$

b)

$x\in\left(\frac{4}{5},\ 3\right]$

c)

$x\in\left[\frac{4}{5},\ 3\right)$

d)

$x\in\left[\frac{4}{5},\ 3\right]$

28.

What is the solution to the inequality $6-x-x^2\le0\ ?$

a)

$x\le-3$ or $x\ge2$

b)

$x\le-2$ or $x\ge3$

c)

$-3\le x\le2$

d)

$-2\le x\le3$

29.

What is the equation of the given graph?

a)

$f\left(x\right)=-\left|x-4\right|+3$

b)

$f\left(x\right)=-2\left|x+4\right|+3$

c)

$f\left(x\right)=-\left|x+4\right|+3$

d)

$f\left(x\right)=-2\left|x-4\right|+3$

e)

$f\left(x\right)=-\left|2x-4\right|+3$

30.

Let $f\left(x\right)=\frac{2}{3-x}$ and $g\left(x\right)=x-5\ .$

What is the domain of $f\left(g\left(x\right)\right)$ ?

a)

All real $x$

b)

$x\ne2$

c)

$x\ne3$

d)

$x\ne8$

e)

$x\ne5$

Ch 3 - Graphs and equations

Total questions: 30

Worksheet time: 45mins

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