A function $$f(x) is $$one-to-one if $$f(x_1$) \neq f(x_2$)$$ whenever $$x_1$$ \neq $$x_2$$

Question 1

Which of the following transformations will shift the graph of $$f(x)$$ vertically upward by $$c$$ units?

Accepted Answer

$$f(x) + c$$

Question 2

Given $$f(x) = 2\sin(3(x - \frac{\pi}{4})) + 1$$, what is the amplitude of the function?

Accepted Answer

$$2$$

Question 3

Which of the following is the correct definition of a one-to-one function?

Accepted Answer

A function $$f(x) is $$one-to-one if $$f(x_1$) 
eq f(x_2$)$$ whenever $$x_1$$ 
eq $$x_2$$

Question 4

What is the domain of $$\cos$$^{-1}$$(x)$$?

Accepted Answer

$$[-1, 1]$$

Question 5

What is the range of $$\cos$$^{-1}$$(x)$$?

Accepted Answer

$$[0, \pi]$$

Question 6

If $$f(x) is $$invertible, which of the following must be true?

Accepted Answer

$$f is $$one-to-one

Question 7

Given $$f(x) = x^3$ + 2$$, find $$f^{-1}(x$$)$$.

Accepted Answer

$$f^{-1}(x$$) = \sqrt[3]{x - 2}$$

Question 8

Which transformation reflects the graph of $$f(x)$$ about the $$y-$$axis?

Accepted Answer

$$f(-x)$$

Question 9

Suppose $$f(x) = \sin(x). $$Which property changes if we consider $$f(x) + c$$ for $$c \u003e 0$$?

Accepted Answer

The $$y-$$intercept

Question 10

If $$f(x) = 3x - 5$$, what is $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 5}{3}$$

Question 11

Which transformation compresses the graph of $$f(x)$$ horizontally by a factor of $$c$$ ($$c \u003e 1$$)?

Accepted Answer

$$f(cx)$$

Question 12

Given $$f(x) = \sin(x)$$, what is the period of $$f(x) = \sin(2x)$$?

Accepted Answer

$$\pi$$

Question 13

Which of the following is NOT a necessary condition for a function to have an inverse?

Accepted Answer

The function must be even

Question 14

If $$f(x) = |x|$$, does $$f$$ have an inverse? Why or why not?

Accepted Answer

No, because $$f(x) is $$not one-to-one

Question 15

Given $$f(x) = A\sin(B(x - w)) + C$$, what is the formula for the period of the function?

Accepted Answer

$$\frac{2\pi}{|B|}$$

Question 16

Which transformation reflects the graph of $$f(x)$$ about the $$x-$$axis?

Accepted Answer

$$-f(x)$$

Transformations and Inverses of Functions in Precalculus

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