Question 1

Which of the following relations is a function?

Accepted Answer

$$\{(1,2), (2,3), (3,4)\}$$

Question 2

Given the function $$f(x) = \sqrt{x-2}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$[2, \infty)$$

Question 3

Which of the following equations represents a circle centered at $$(2, -3)$$ with radius $$4$$?

Accepted Answer

$$(x-2)^2$$ + $$(y+3)^2 = 16$

Question 4

If $$f(x) = x^2$ and g(x) = x+1$, what is (f+g)(x$$)$$?

Accepted Answer

$$x^2 + x + 1$

Question 5

Which of the following graphs passes the vertical line test and is therefore a function?

Accepted Answer

A parabola opening upwards

Question 6

Given $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is the domain of (f$$ \circ g)(x)$$?

Accepted Answer

$$[0, \infty)$$

Question 7

Which transformation describes $$y = f(x-3) + 2$$ compared to $$y = f(x)$$?

Accepted Answer

Shift right 3 units, up 2 units

Question 8

What is the range of the function $$f(x) = \sqrt{x+4}$$?

Accepted Answer

$$[0, \infty)$$

Question 9

If $$f(x) = x^2$ and g(x) = 2x$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$4x^2$$

Question 10

Given the equation $$x^2$$ + $$y^2 = 9$, which of the following statements is true?

Accepted Answer

It is not a function because it fails the vertical line test.

Question 11

What is the domain of $$f(x) = \frac{1}{x-5}$$?

Accepted Answer

$$(-\infty, 5) \cup (5, \infty)$$

Question 12

If $$f(x) = |x|$$, which transformation results in $$g(x) = -|x| + 3$$?

Accepted Answer

Reflect over the $$x-$$axis and shift up 3 units

Question 13

Given $$f(x) = x^2$ and g(x) = x+1$, what is (f-g)(x$$)$$?

Accepted Answer

$$x^2 - x - 1$

Question 14

Which of the following is the correct interval notation for the domain of $$f(x) = \sqrt{7-x}$$?

Accepted Answer

$$(-\infty, 7]$$

Question 15

If $$f(x) = x^2$ and g(x) = x-4$, what is (f$$ \div g)(x)$$?

Accepted Answer

$$\frac{x^2$}{x-4}$$

Question 16

Which of the following describes the transformation $$y = -f(x+2)$$?

Accepted Answer

Reflect over the $$x-$$axis and shift left 2 units

Question 17

Given $$f(x) = x^2$ and g(x) = 3x-6$, what is the domain of (f$$ \cdot g)(x)$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 18

Which of the following is the correct standard form of a circle with center $$(-1, 2)$$ and radius $$5$$?

Accepted Answer

$$(x+1)^2$$ + $$(y-2)^2 = 25$

Question 19

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is the domain of (g$$ \circ f)(x)$$?

Accepted Answer

$$(-\infty, \infty)$$

Functions and Graphs: Precalculus Study Notes

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