Question 1

Which of the following is the correct formula for the distance between Kiara and Matias after $$t$$ hours, if Kiara drives east at 35 mph and Matias drives north at 40 mph, starting from the same point?

Accepted Answer

$$d(t) = \sqrt{(35t)^2$ + (40t)^2$}$$

Question 2

Which of the following is the graph of the basic squaring function?

Accepted Answer

$$y = x^2$

Question 3

Given the piecewise function $$f(x) = \begin{cases} x+2 & 	ext{if } x \u003c 0 \ x^2$ & 	ext{if } x \geq 0 \end{cases}$$, what is $$f(-3)$$?

Accepted Answer

Question 4

Which of the following best describes the transformation from the basic square root function $$y = \sqrt{x} to$$ $$f(x) = \sqrt{x+3}$$?

Accepted Answer

Shifted 3 units to the left

Question 5

What is the domain of the function $$d(t) = \sqrt{(35t)^2$ + (40t)^2$}$$, where $$t$$ represents time in hours?

Accepted Answer

$$t \geq 0$$

Question 6

Which of the following is the greatest integer less than or equal to $$-2.7$$?

Accepted Answer

$$-3$$

Question 7

Given the piecewise function $$g(x) = \begin{cases} \frac{1}{3}x + 3 & x \u003c 3 \ -x & x \geq 3 \end{cases}$$, what is $$g(4)$$?

Accepted Answer

$$-4$$

Question 8

Which of the following is the correct graph for the absolute value function?

Accepted Answer

$$y = |x|$$

Question 9

A function is defined as $$f(x) = 3 - x^2$. Which transformation has been applied to the basic squaring function to obtain this function?

Accepted Answer

Reflected across the x-axis and shifted up 3 units

Question 10

Evaluate the greatest integer function $$f(x) = \lfloor x \rfloor at$$ $$x = 2.99.$$

Accepted Answer

$$2$$

Question 11

Which of the following is NOT a basic function from the library of functions?

Accepted Answer

$$y = \sin(x)$$

Question 12

Given the piecewise function $$h(x) = \begin{cases} 2x - 1 & x \u003c 1 \ x^2$ & x \geq 1 \end{cases}$$, what is $$h(1)$$?

Accepted Answer

$$2$$

Question 13

Which of the following real-world scenarios can be modeled by a piecewise function?

Accepted Answer

A taxi fare that charges a flat rate for the first mile and a different rate for each additional mile

Question 14

If $$f(x) = \sqrt{x+3}$$, what is the domain of $$f$$?

Accepted Answer

$$x \geq -3$$

Question 15

Which of the following is the correct formula for the reciprocal function?

Accepted Answer

$$y = \frac{1}{x}$$

Question 16

Evaluate the piecewise function $$f(x) = \begin{cases} x+2 & x \u003c 0 \ x^2$ & x \geq 0 \end{cases} at$$ $$x = 2.$$

Accepted Answer

$$4$$

Question 17

Which of the following best describes the graph of $$y = \lfloor x \rfloor$$?

Accepted Answer

A step function with jumps at every integer

Question 18

If $$f(x) = |x|$$, which of the following statements is true?

Accepted Answer

$$f(x) is $$always nonnegative

Question 19

Which of the following is the correct formula for the cube root function?

Accepted Answer

$$y = \sqrt[3]{x}$$

Chapter 2: More on Functions – College Algebra Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard