Quiz about Math 10A Review (pre-midterm)

Question 1

What is the purpose of the vertical line test?

Accepted Answer

To verify if a graph represents a function

Answer

To determine if a function is increasing

Answer

To check if a function is one-to-one

Answer

To find the x-intercept

Question 2

In a composite function g(f(x)), what must be true about f(x)?

Accepted Answer

f(x) must be in the domain of g

Answer

f(x) must be in the range of g

Answer

f(x) must be equal to g(x)

Answer

f(x) must be greater than g(x)

Question 3

What is the domain of the composite function g(f(x))?

Accepted Answer

domain of f(x)

Answer

range of f(x)

Answer

range of g(x)

Answer

domain of g(x)

Question 4

What is the characteristic of an odd function?

Accepted Answer

f(-x) = -f(x)

Answer

f(x) = f(-x)

Answer

f(x) = -f(x)

Answer

f(x) = -f(-x)

Question 5

Name the transformation: f(x-c)

Accepted Answer

horizontal shift right

Answer

vertical shift up

Answer

vertical shift down

Answer

horizontal shift left

Question 6

Name the transformation: 0.5*f(x)

Accepted Answer

vertical compress

Answer

vertical stretch

Answer

horizontal stretch

Answer

horizontal compress

Question 7

Which of the following functions has a period of 2pi?

Accepted Answer

sin(x)

Accepted Answer

cos(x)

Accepted Answer

csc(x)

Answer

tan(x)

Question 8

What is the purpose of the horizontal line test?

Accepted Answer

To check if a function is one-to-one

Answer

To determine if a function is increasing

Answer

To find the x-intercept

Answer

To verify if a graph represents a function

Question 9

To get an inverse trig function, the domain of the original function must be restricted.

Which of the following is false?

Accepted Answer

restrict domain of sin and tan to [-pi/2, pi/2]

Answer

restrict domain of cos and sin to [0,pi]

Answer

restrict domain of tan to (-pi/2, pi/2)

Answer

restrict domain of sin to [-pi/2, pi/2]

Question 10

Which of the following does the slope of a tangent line represent (Select two)

Accepted Answer

instantaneous rate of change

Accepted Answer

Answer

average rate of change

Question 11

"the limit of f(x) as x approaches a is L"

Explain what this limit means:

Accepted Answer

The values of f(x) approach L as x approaches a

Answer

the function f(x) is undefined at x=a

Answer

the function f(x) is discontinuous at x=a

Answer

The value of f(a) = L

Question 12

The limit exists if a one-sided limit exists.

Accepted Answer

False

Answer

True

Question 13

The limit exists if the two sided limit goes to infinity

Accepted Answer

False

Answer

True

Question 14

What are the conditions for a function f(x) to be continuous at point x=c?

Accepted Answer

All of the above

Answer

Answer

Answer

Question 15

Which of the following is the limit definition of the derivative of a function f(x) at a point x=a?

Accepted Answer

Question 16

What is the formula for the slope of a secant line between two points on a function f(x)?

Accepted Answer

Question 17

if f'(x) is positive on (a, b), then:

Accepted Answer

the function f is increasing on (a, b)

Answer

the function f is decreasing on (a, b)

Answer

the function f is concave up

Answer

the function f is concave down

Question 18

True or false: If f'(c) = 0, then the function f is neither increasing nor decreasing; the tangent line at c is a horizontal line.

Accepted Answer

True

Answer

False

Question 19

Derivative rules: which of the following is the constant multiple rule?

Accepted Answer

Question 20

Derivatives: Which of the following is the quotient rule?

Accepted Answer

Question 21

if f(x) = sin(x), the eighth derivative of f(x) = ____?

Accepted Answer

sin(x)

Answer

cos(x)

Answer

-cos(x)

Answer

-sin(x)

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