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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

`\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