Functions Chapter Review
Chapter
Chapter 1
Section
Functions Chapter Review
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Solutions 34 Videos

For each relation, determine the domain and range and whether the relation is a function. Explain your reasoning.

(a) {(-3, 0), (-1, -1), (0, 1), (4, 5), (0, 6) }

(b) y = 4-x

(c)

(d) x^2 + y^2 = 16

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1.30mins
Q1

What rule can you use to determine, from the graph of a relation, whether the relation is a function? Graph the relation and determine which are functions.

{(-2,1), (1, 1), (0, 0), (1, -1), (1, -2), (2, -2)}

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0.56mins
Q2a

What rule can you use to determine, from the graph of a relation, whether the relation is a function? Graph the relation and determine which are functions.

y = 4- 3x

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0.39mins
Q2b

What rule can you use to determine, from the graph of a relation, whether the relation is a function? Graph the relation and determine which are functions.

y = (x - 2)^2+ 4

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0.33mins
Q2c

What rule can you use to determine, from the graph of a relation, whether the relation is a function? Graph the relation and determine which are functions.

x^2 + y^2 = 1

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0.52mins
Q2d

What rule can you use to determine, from the graph of a relation, whether the relation is a function? Graph the relation and determine which are functions.

y = \frac{1}{x}

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0.23mins
Q2e

What rule can you use to determine, from the graph of a relation, whether the relation is a function? Graph the relation and determine which are functions.

y = \sqrt{x}

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0.16mins
Q2f

Sketch the graph of a function whose domain is the set of real numbers and whose range is the set of real numbers less than or equal to 3.

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0.48mins
Q3

If f(x) = x^2 + 3x -5 and g(x) = 2x - 3, determine each.

\displaystyle \begin{array}{ccccccc} &a) & f(-1) & d)& f(2b)\\ &b) &f(0) & e)& g(1- 4a)\\ &c)& g(\frac{1}{2}) & f) & x \text{ when } f(x) = g(x) \\ \end{array}

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1.41mins
Q4

(a) Graph the function f(x) =-2(x - 3)^2 + 4, and state its domain and range.

(b) What does f(1) represent on the graph?

(c) Use the equation to determine each of the following.

\displaystyle \begin{array}{cccccc} &(i) &f(3) -f(2) &(iii) & f(1-x) \\ &(ii) &2f(5) + 7 &&\\ \end{array}

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1.08mins
Q5

If f(x) = x^2 -4x + 3, determine the input(s) for x whose output is f(x) = 8

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0.29mins
Q6

A ball is thrown upward from the roof of a building 60 m tall. The ball reaches a height of 80 m above the ground after 2 s and hits the ground 6 s after being thrown.

(a) Sketch a graph that shows the height of the ball as a function of time.

(b) State the domain and range of the function.

(c) Determine an equation for the function.

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7.07mins
Q7

State the domain and range of each function.

(a) f(x) = 2(x - 1)^2 + 3

(b) f(x) = \sqrt{2x + 4}

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1.07mins
Q8

A farm has 540 m of fencing to enclose a rectangular area and divide in into two sections as shown.

(a) Write an equation to express the total area enclosed as a function to the width.

(b) Determine the domain and range of this area function.

(c) Determine the dimensions that give the maximum area.

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3.55mins
Q9

Determine the inverse functions for the following algebraically for (b) and graphically for (a).

(a) \displaystyle f(x) = 2x - 5

(b) \displaystyle f(x) = 4- \frac{1}{2}x

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1.27mins
Q10ab

For a fundraising event, a local charity organization expects to receive \$15 000 from corporate sponsorship, plus \$30 from each person who attends the event.

(a) Use function notation to express the total income from the event as a function of the number of people who attend.

(b) Suggest a reasonable domain and range for the function in part (a). Explain your reasoning.

(c) The organizers want to know how many tickets they need to sell to reach their fundraising goal. Create a function to express the number of people as a function of expected income. State the domain of this new function.

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1.56mins
Q11

In each graph, a parent function has undergone a transformation of the form f(kx). Determine the equations of the transformed functions graphed in red. Explain your reasoning.

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0.45mins
Q12a

In each graph, a parent function has undergone a transformation of the form f(kx). Determine the equations of the transformed functions graphed in red. Explain your reasoning.

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2.19mins
Q12b

For the set of functions, transform the graph of f(x) to sketch g(x) and h(x), and state the domain and range of each function.

\displaystyle f(x) = x^2, g(x) = (\frac{1}{2}x)^2, h(x) = -(2x)^2

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1.12mins
Q13a

For the set of functions, transform the graph of f(x) to sketch g(x) and h(x), and state the domain and range of each function.

\displaystyle f(x) =|x|, g(x) = |-4x|, h(x) = |\frac{1}{4}x|

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1.15mins
Q13b

Three transformations are applied to y= x^2: a vertical stretch by the factor 2, a translation 3 units right, and a translation 4 units down.

(a) Is the order of the transformations important?

(b) Is there any other sequence of these transformations that could produce the same result?

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1.39mins
Q14

The point (1, 4) is on the graph of y=f(x). Determine the coordinates of the image of this point on the graph of y = 3f[-4(x + 1)] -2.

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0.50mins
Q15

State the transformation mapping and describe all the transformation for y = -2f(\frac{1}{3}x + 4)- 1.

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1.38mins
Q16a

Graph y = -2f(\frac{1}{3}x + 4) - 1 for f(x) = x^2.

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1.23mins
Q16b

Write the equation for the transformed function, sketch its graph, and state its domain and range.

The graph of f(x) = \sqrt{x} is compressed horizontally by the factor \frac{1}{2}, reflected in the y-axis, and translated 3 units right and 2 unit down.

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2.18mins
Q17a

Write the equation for the transformed function, sketch its graph, and state its domain and range.

The graph of y = \frac{1}{x} is stretched vertically by the factor 3, reflected in the x-axis, and translated 34 units left and 1 unit up.

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3.01mins
Q17b

If f(x) = (x -4)(x + 3), determine the x-intercepts of the function.

\displaystyle y =f(x)

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0.24mins
Q18a

If f(x) = (x -4)(x + 3), determine the x-intercepts of the function.

\displaystyle y = -2f(x)

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0.23mins
Q18b

If f(x) = (x -4)(x + 3), determine the x-intercepts of the function.

\displaystyle y = f(-\frac{1}{2}x)

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0.41mins
Q18c

If f(x) = (x -4)(x + 3), determine the x-intercepts of the function.

\displaystyle y = f(-(x + 1))

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1.06mins
Q18d

A function f(x) has domain \{x \in \mathbb{R} \vert x \geq -4\} and range \{ y\in \mathbb{R}| y < -1\}. Determine the domain and range of each function.

y = 2f(x)

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0.29mins
Q19a

A function f(x) has domain \{x \in \mathbb{R} \vert x \geq -4\} and range \{ y\in \mathbb{R}| y < -1\}. Determine the domain and range of each function.

y = 3f(x + 1) + 4

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1.02mins
Q19b

A function f(x) has domain \{x \in \mathbb{R} \vert x \geq -4\} and range \{ y\in \mathbb{R}| y < -1\}. Determine the domain and range of each function.

y = f(-x)

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0.41mins
Q19c

A function f(x) has domain \{x \in \mathbb{R} \vert x \geq -4\} and range \{ y\in \mathbb{R}| y < -1\}. Determine the domain and range of each function.

y = -2f(-x + 5) + 1

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1.10mins
Q19d