Question 1

Given the relation $$\{(1, 7), (2, 8), (3, 3)\}$$, determine if it is a function. If so, state its domain and range.

Accepted Answer

Function. Domain: $$\{1, 2, 3\}$$, Range: $$\{7, 8, 3\}$$

Question 2

Evaluate $$g(0)$$ for the function $$g(x) = x^3$ + 3.$$

Accepted Answer

$$3$$

Question 3

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

Accepted Answer

$$2x + h + 1$$

Question 4

Evaluate and simplify $$h(3a)$$ for $$h(x) = x^4$ + 5x^2$ - 11.$$

Accepted Answer

$$81a^4$$ + $$45a^2 - 11$

Question 5

Does the equation $$f(y) - 2y = 6$$ define $$y as a $$function of $$x$$?

Accepted Answer

The equation does not define $$y as a $$function of $$x.$$

Question 6

Given the graph of a line passing through $$(-2, 0)$$ and $$(0, -6)$$, what are the $$x- $$and $$y-$$intercepts?

Accepted Answer

$$(-2, 0)$$ and $$(0, -6)$$

Question 7

Which of the following sets represents the range of the relation $$\{(1, 7), (2, 8), (3, 3)\}$$?

Accepted Answer

$$\{7, 8, 3\}$$

Question 8

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

Accepted Answer

$$1$$

Question 9

Which of the following best describes the domain of $$g(x) = x^3$ + 3$$?

Accepted Answer

All real numbers

Question 10

Suppose $$h(x) = x^4$ + 5x^2$ - 11. $$What is $$h(-2)$$?

Accepted Answer

$$9$$

Question 11

A real-world scenario: The height $$h (in $$meters) of a ball thrown upward is given by $$h(t) = -4.9t^2$ + 20t + 1.5. $$What is the height after $$2$$ seconds?

Accepted Answer

$$h(2) = -4.9(2)^2$ + 20(2) + 1.5 = 32.9$$

Question 12

Which of the following is NOT a function?

Accepted Answer

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

Question 13

If $$f(x) = x^2$ + x + 1$$, what is the average rate of change from $$x = 1 to$$ $$x = 3$$?

Accepted Answer

$$5$$

Question 14

Given $$g(x) = x^3$ + 3$$, for which value of $$x$$ does $$g(x) = 11$$?

Accepted Answer

$$2$$

Graphs and Coordinates: Functions, Domains, and Intercepts

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