Free Printable Pre-Cal: CSC and SEC graphs

1.

A cosecant function has a period of

4\pi

. Which of the following could be this function?

a)

$y=\csc\left(4\pi x\right)$

b)

$y=\csc\left(4x\right)$

c)

$y=\csc\left(\frac{1}{4}x\right)$

d)

$y=\csc\left(\frac{1}{2}x\right)$

2.

The __________ represents the distance from the baseline of sine/cosine to the max and min of the curve.

a)

Period

b)

Frequency

c)

Max/Min

d)

Amplitude

3.

What is the range of $y=3\sin2x$ ?

a)

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

b)

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

c)

$\left(-3,\ 3\right)$

d)

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

4.

What is the amplitude of

$y=-5\csc2x$ ?

a)

5

b)

-5

c)

$\frac{1}{4}$

d)

None

5.

What is the minimum value in the range of $y=2\sin\frac{1}{3}x$ ?

a)

2

b)

$\frac{1}{3}$

c)

$6\pi$

d)

-2

6.

Describe the transformations of y = - 6 csc ( 2x + π ) - 11

Select all that apply?

a)

down 11

b)

reflection over the x - axis

c)

phase shift = π/2 to the right

d)

period = 1

e)

Amplitude is 6

7.

Describe the transformations of y = 2cot ( 3x - 2π ) + 4

a)

down 4 units

b)

phase shift = 2π/3 to the right

c)

vertical stretch by a factor of 2

d)

reflection over the x - axis

e)

per = π/3

8.

Determine the period for this graph:

a)

$\pi$

b)

$2\pi$

c)

$4\pi$

d)

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

e)

$\frac{\pi}{2}$

9.

Which function below matches the graph?

a)

$y=\csc\left(x+\frac{\pi}{2}\right)$

b)

$y=\sec\left(x+\frac{\pi}{2}\right)$

c)

$y=\sec\left(x-\frac{\pi}{2}\right)$

d)

$y=\csc\left(x-\frac{\pi}{2}\right)$

10.

What is the range for y = csc x ?

Hint: graph the equation if necessary

a)

All real numbers

b)

All real numbers except odd multiples of π /2

c)

All real numbers except multiples of π

d)

All real numbers between -1 and 1, inclusive; [-1,1]

e)

(-∞, -1] U [1, ∞)

11.

What is the x-intercept of

y = -2csc ( x + π )

a)

0

b)

π

c)

no x-intercept

d)

$\frac{\pi}{2}$

12.

Write an equation for the graph.

a)

y = 2sec(x)

b)

y = -2sec(x)

c)

y = 2csc(x)

d)

y = -2csc(x)

13.

What is the range of the graph?

a)

(-∞, ∞)

b)

(-∞, -2] ∪ [2, ∞)

c)

[ -2, 2]

d)

(-∞, -2)∪ (2, ∞)

14.

Which parent function meets the following requirements?

a)

tangent

b)

cotangent

c)

secant

d)

cosecant

15.

Which two inverse trig functions have similar looking graphs?

a)

cosecant and cotangent

b)

secant and cotangent

c)

cosecant and secant

16.

Which value represents a horizontal shift (left and right) in the following function y=a*sin(bx-c)+d?

a)

a

b)

b

c)

c

d)

d

17.

Which of the following is an asymptote for secant?

a)

x= π

b)

x = 3π / 2

c)

x = -2π

d)

x = 0

18.

Describe the zeros for cosecant.

a)

All real numbers

b)

Odd multiples of π / 2

c)

All multiples of π

d)

There are none

Pre-Cal: CSC and SEC graphs

Total questions: 18

Worksheet time: 18mins

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