Q: Which of the following is the piecewise function for the T-shirt cost: $$C(x) is$$ $$10$$ per shirt for $$x \u003c 50$$, $$9$$ per shirt for $$50 \leq x \u003c 100$$, and $$8$$ per shirt for $$x \geq 100$$?

$$C(x) = \begin{cases} 10x & x \u003c 50 \\ 9x & 50 \leq x \u003c 100 \\ 8x & x \geq 100 \end{cases}$$

Question 1

Which of the following numbers is irrational?

Accepted Answer

$$\pi$$

Question 2

Given the points $$A(-2, 4)$$ and $$B(0, -3)$$, in which quadrant does point $$A$$ lie?

Accepted Answer

Quadrant II

Question 3

If $$a = 5$$ and $$c = 8$$, use the Pythagorean Theorem to find $$b.$$

Accepted Answer

$$b = \sqrt{39}$$

Question 4

Which of the following relations is a function?

Accepted Answer

{$$(5,1), (3,2), (4,9), (7,6)$$}

Question 5

What is the slope of the line passing through the points $$(1,2)$$ and $$(-3,7)$$?

Accepted Answer

$$-\frac{5}{4}$$

Question 6

A company produces 25 heaters for $$7000 and 30 heaters for 8300. $$What is the linear cost function $$y in $$terms of $$x ($$number of heaters)?

Accepted Answer

$$y = 260x + 5000$$

Question 7

Solve for $$x$$: $$4(2x-3) = 8(2x+1)$$

Accepted Answer

No solution

Question 8

Which equation represents a line parallel to $$5x + y - 4 = 0$$ and passing through $$(-1, -3)$$?

Accepted Answer

Question 9

Given the function $$f(x) = 2x^2$ - 7x + 3$$, what is the simplified form of the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$4x + 2h - 7$$

Question 10

Which transformation results in the graph of $$y = \sqrt{x}$$ being shifted left 2 units and up 3 units?

Accepted Answer

$$y = \sqrt{x+2} + 3$$

Question 11

Let $$f(x) = |x-2| + 1. $$What is the domain and range of $$f(x)$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$[1, \infty)$$

Question 12

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$ - 8$$

Question 13

Solve the absolute value equation: $$|3x - 4| = 0$$

Accepted Answer

$$x = \frac{4}{3}$$

Question 14

Let $$f(x) = x^2$ and g(x) = x + 1$. What is (f$$ \circ g)(x)$$?

Accepted Answer

$$(x+1)^2$$

Question 15

A T-shirt company has a fixed cost of $$40,000 and a variable cost of 3$ per T-shirt. If the company sells T-shirts for 10$ each, how many T-shirts must be sold to break even?

Accepted Answer

$$5,714$$

Question 16

Which of the following describes the transformation from $$f(x) = x^2$ to g(x$$) = $$2(x-1)^2 + 3$?

Accepted Answer

Shift right 1, vertical stretch by 2, shift up 3

Question 17

Which of the following is the piecewise function for the T-shirt cost: $$C(x) is$$ $$10$$ per shirt for $$x \u003c 50$$, $$9$$ per shirt for $$50 \leq x \u003c 100$$, and $$8$$ per shirt for $$x \geq 100$$?

Accepted Answer

$$C(x) = \begin{cases} 10x & x \u003c 50 \ 9x & 50 \leq x \u003c 100 \ 8x & x \geq 100 \end{cases}$$

Question 18

If $$f(x) = x^2$ with domain $$[-1,2]$$ and range $$[0,4]$$, what is the domain and range of f(x-4$$)$$?

Accepted Answer

Domain: $$[3,6]$$, Range: $$[0,4]$$

Precalculus Study Guide: Real Numbers, Functions, Linear Equations, Transformations, and Piecewise Functions

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