Mid Chapter Review on Functions
Chapter
Chapter 1
Section
Mid Chapter Review on Functions
Solutions 23 Videos

Determine whether each relation is a function, and state its domain and range.

Q1a

Determine whether each relation is a function, and state its domain and range.

\displaystyle y = 2x + 3 

Q1b

Determine whether each relation is a function, and state its domain and range.

Q1c

Determine whether each relation is a function, and state its domain and range.

\{(2, 7), (1, 3), (2, 6), (10, -1)\}

Q1d

The height of a bungee jumper above the ground is modelled by the following data.

a) Is the relationship between height and time a function? Explain

b) What is the domain?

c) What is the range?

Q2

Determine the domain and range for each of the following and state whether it is a function:

\displaystyle f(x) = 3x + 1 

Q3a

Determine the domain and range for each of the following and state whether it is a function:

\displaystyle x^2+ y^2 = 9 

Q3b

Determine the domain and range for each of the following and state whether it is a function:

\displaystyle y = \sqrt{5 -x} 

Q3c

Determine the domain and range for each of the following and state whether it is a function:

\displaystyle x^2 -y = 2 

Q3d

Arrange the following values in order, from least to greatest:

\displaystyle |-3|, -|3|, |5|, |-4|, |0| 

Q4

Sketch the graph of each function.

\displaystyle f(x) = |x| + 3 

Q5a

Sketch the graph of each function.

\displaystyle f(x) = |x| - 2 

Q5b

Sketch the graph of each function.

\displaystyle f(x) = |-2x| 

Q5c

Sketch the graph of each function.

\displaystyle f(x) = |0.5x| 

Q5d

Determine a parent function that matches each set of characteristics.

a) The graph is neither even nor odd, and as x \to \infty, y \to \infty

b) (-\infty, 0), and (0, \infty) are both intervals of decrease.

c) The domain is [0, \infty)

Q6

Determine algebraically if each function is even, odd, or neither.

\displaystyle f(x) = |2x| 

Q7a

Determine algebraically if each function is even, odd, or neither.

\displaystyle f(x) = (-x)^2 

Q7b

Determine algebraically if each function is even, odd, or neither.

\displaystyle f(x) = x + 4 

Q7c

Determine algebraically if each function is even, odd, or neither.

\displaystyle f(x) = 4x^5 +3x^3 -1 

Q7d

The set of characteristics describes a parent function that has been shifted. Draw a possible graph, and state whether the graph is continuous.

There is a vertical asymptote at x = 1 and a horizontal asymptote at y = 3.

Q8a

The set of characteristics describes a parent function that has been shifted. Draw a possible graph, and state whether the graph is continuous.

The range is \{f(x) \in \mathbb{R} \Vert -3 \leq f(x) \leq -1\}

Q8b

The set of characteristics describes a parent function that has been shifted. Draw a possible graph, and state whether the graph is continuous.

The interval of increase is (-\infty, \infty), and there is a horizontal asymptote at y =-10.

• The function has zeros at x = -3 0, and 3.
• The function is increasing on the intervals x\in (-\infty, -2) or x\in (2, \infty)
• The function is decreasing on the interval x\in(-2, 2).