1.8 Review Exercise
Chapter
Chapter 1
Section
1.8
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11mathHarcourt1.8 49 Videos

State the domain and range for each of the following relations.

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

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Q1a

State the domain and range for each of the following relations.

\displaystyle \left\{(-2,0),\left(-1, \frac{1}{2}\right),(0,1),\left(-1,-\frac{1}{2}\right),(0,-1)\right\}

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Q1b

State the domain and range for each of the following relations.

\displaystyle x+2 y=4

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Q1c

State the domain and range for each of the following relations.

\displaystyle y=4-x^{2}

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Q1d

State the domain and range for each of the following relations.

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

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Q1e

State the domain and range for each of the following relations.

\displaystyle f(x)=\sqrt{x+1}

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Q1f

For each part of Question 1, find the inverse relation and its domain and range. Which of these inverses are functions?

a. \displaystyle \{(-2,1),(-1,0),(0,-1),(1,0),(2,1)\}

b. \displaystyle \left\{(-2,0),\left(-1, \frac{1}{2}\right),(0,1),\left(-1,-\frac{1}{2}\right),(0,-1)\right\}

c. \displaystyle x+2 y=4

d. \displaystyle y=4-x^{2}

e. \displaystyle f(x)=\frac{1}{2} x+1

f. \displaystyle f(x)=\sqrt{x+1}

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Q2

For each of the following graphed relations,

state the domain and range;

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Q3a

For each of the following graphed relations,

sketch the inverse relation

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Q3b

The graph at the right gives the position of the elevator in a building over several minutes. Explain what has happened here.

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Q4

The height \displaystyle h , in metres, of a projectile fired vertically is graphed against time \displaystyle t , in seconds, as shown.

What is the maximum height of the projectile?

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Q5a

The height \displaystyle h , in metres, of a projectile fired vertically is graphed against time \displaystyle t , in seconds, as shown.

When does it reach this height?

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Q5b

The height \displaystyle h , in metres, of a projectile fired vertically is graphed against time \displaystyle t , in seconds, as shown.

What does the \displaystyle h  -intercept represent?

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Q5c

The height \displaystyle h , in metres, of a projectile fired vertically is graphed against time \displaystyle t , in seconds, as shown.

What does the \displaystyle t  -intercept represent?

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Q5d

For \displaystyle f(x)=x^{2}-1

find \displaystyle f(-2), f(-1) , and \displaystyle f(2)

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Q6a

For \displaystyle f(x)=x^{2}-1

state the domain and range for \displaystyle f(x) .

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Q6b

For \displaystyle f(x)=\sqrt{x+3}

find \displaystyle f(1), f(-2) , and \displaystyle f(-4)

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Q7a

For \displaystyle f(x)=\sqrt{x+3}

state the domain and range for \displaystyle f(x)

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Q7b

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

find \displaystyle f(-2), f(0) , and \displaystyle f\left(\frac{1}{2}\right)

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Q8a

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

state the domain and range for \displaystyle f(x)

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Q8b

From the graph of \displaystyle f(x)  shown,

find \displaystyle f(-2), f\left(\frac{1}{2}\right) , and \displaystyle \frac{1}{f(2)} ;

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Q9a

From the graph of \displaystyle f(x)  shown,

sketch the graph of the inverse of \displaystyle f(x)

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Q9b

\displaystyle f(x)=2 x+1  and \displaystyle g(x)=x^{2}+1 . Determine each of the following:

\displaystyle f(1)+g(1)

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Q10a

\displaystyle f(x)=2 x+1  and \displaystyle g(x)=x^{2}+1 . Determine each of the following:

\displaystyle f(-1) \cdot g(-1)

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Q10b

\displaystyle f(x)=2 x+1  and \displaystyle g(x)=x^{2}+1 . Determine each of the following:

\displaystyle f(g(1))

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Q10c

\displaystyle f(x)=2 x+1  and \displaystyle g(x)=x^{2}+1 . Determine each of the following:

\displaystyle g(f(-1))

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Q10d

Using the graph for \displaystyle y=f(x)  as shown, graph the following:

\displaystyle f(x-2)

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Q11a

Using the graph for \displaystyle y=f(x)  as shown, graph the following:

\displaystyle f(x+2)

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Q11b

Using the graph for \displaystyle y=f(x)  as shown, graph the following:

\displaystyle 2 f(x)

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Q11c

Using the graph for \displaystyle y=f(x)  as shown, graph the following:

\displaystyle f(2 x)

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Q11d

Using the graph for \displaystyle y=f(x)  as shown, graph the following:

\displaystyle -f(x)

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Q11e

Using the graph for \displaystyle y=f(x)  as shown, graph the following:

\displaystyle f(-x)

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Q11f

Using the graph for \displaystyle y=f(x)  as shown, graph the following:

\displaystyle 2 f(x-1)

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Q11g

Using the graph for \displaystyle y=f(x)  as shown, graph the following:

\displaystyle 2-f(2 x)

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Q11h

Given \displaystyle f(x)=2 x-4 , determine the equation of its inverse.

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Q12

Give the vertex and range for each. Sketch the graph of each function.

\displaystyle y=-2(x-2)^{2}+1

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Q13a

Give the vertex and range for each. Sketch the graph of each function.

\displaystyle y=4(x+4)^{2}

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Q13b

Give the vertex and range for each. Sketch the graph of each function.

\displaystyle y=16-x^{2}

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Q13c

Give the equation for each of the following parabolas.

Vertex \displaystyle (-1,1) , opening up, congruent to \displaystyle y=-x^{2}

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Q14a

Give the equation for each of the following parabolas.

Vertex \displaystyle (2,0) , range \displaystyle y \leq 0 , congruent to \displaystyle y=2 x^{2}

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Q14b

Give the equation for each of the following parabolas.

Axis \displaystyle x=-2 , range \displaystyle y \geq-3 , congruent to \displaystyle y=\frac{x^{2}}{2} .

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Q14c

State the domain and range for each of the following:

\displaystyle y=2(x-1)^{2}-3

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Q15a

State the domain and range for each of the following:

\displaystyle y=2 \sqrt{x-1}-3

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Q15b

State the domain and range for each of the following:

\displaystyle y=\frac{2}{x-1}-3

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Q15c

Sketch graphs for each of the following:

\displaystyle y=2 x^{2}-1

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Q16a

Sketch graphs for each of the following:

\displaystyle y=2 \sqrt{x}-1

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Q16b

Sketch graphs for each of the following:

\displaystyle y=\frac{2}{x}-1

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Q16c

For each of the following, sketch the graph and state the equations of the asymptotes.

\displaystyle y=\frac{3}{x-2}+1

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Q17a

For each of the following, sketch the graph and state the equations of the asymptotes.

\displaystyle y=3-\frac{2}{x+1}

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Q17b