Textbook

Functions 11 McGraw-Hill
Chapter

Chapter 1
Section

Practice Test for Functions and Quadratics

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Solutions
28 Videos

Is the following statement true or false?

- Every relation is a special type of function.

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Q1a

Is the following statement true or false?

- Every function is a special type of relation.

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Q1b

Is the following statement true or false?

- For
`f(x) = \frac{3}{x - 2}, x`

can be any real number except`x = 2`

.

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Q1c

Is the following statement true or false?

`\sqrt{81}`

can be fully simplified to`3 \sqrt{9}`

.

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Q1d

Is the following statement true or false?

A quadratic function and a linear function always intersect at least once.

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Q1e

A vertical line test can be used to determine

**A** If a relation is a function

**B** if a relation is constant

**C** if a function is relation

**D** all of the above are true.

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Q2

The range of the function `f(x)= -x^2 + 7`

is

**A** `\{y \in \mathbb{R}, y \geq 7\}`

**B** `\{y \in \mathbb{R}, y \leq 7\}`

**C** `\{y \in \mathbb{R}, y > 0\}`

**D** `\{y \in \mathbb{R}`

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Q3

Which function would produce an output of `y = 9`

for `x = 1`

and for `x = - 1`

.

**A** `y = 2x + 7`

**B** `y = x^2 -3x + 1`

**C** `y = 2x^2 + 7`

**D** All of the above

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Q4

The vertex of `y = -3x^2 + 6x -2`

is

```
\displaystyle
\begin{array}{llll}
&A) &(1, -2) & &B) & (1, 1) \\
&C) & (-1, 1) & &D) &(-1, -2) \\
\end{array}
```

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Q5

Given `f(x) =x^2-6x + 10`

, if `f(a) = 1`

, what is the value of `a`

?

```
\displaystyle
\begin{array}{llll}
&A) &5 & &B) & 3 \\
&C) & 2 & &D) &1 \\
\end{array}
```

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Q6

Sketch a relation that is

a) a function with domain `\{x \in \mathbb{R}\}`

and range `\{y \in \mathbb{R}, -5 \leq y \leq 5\}`

.

b) not a function with domain `\{x\in \mathbb{R}, -5\leq x \leq 5\}`

and range `\{y \in \mathbb{R}, -5 \leq y \leq 5\}`

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Q7

State the domain and the range of each function.

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Q8a

State the domain and the range of each function.

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Q8b

The time needed for a pendulum to make one complete swing is called the period of the pendulum. The period, `T`

, in seconds, for a pendulum of length `l`

, in meters, can be approximated using the function `T = 2\sqrt{l}`

.

a) State the domain and the range of `T`

.

b) Sketch a graph of the relation.

c) Is the relation a function? Explain.

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Q9

Write the ordered pairs that correspond to the mapping diagram. Is this a function?

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Q10

a) Find the vertex of the parabola defined by `f(x) = -\frac{1}{2}x^2 + 4x + 3`

b) Is the vertex a minimum or a maximum? Explain.

c) How many x-intercepts does the function have? Explain.

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Q11

Pat has `30 m`

of fencing to enclose three identical stalls behind the barn, as shown.

a) What dimensions will produce a maximum area for each stall?

b) What it that maximum area of each stall?

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Q12

Simon knows that at `\$ 30`

per ticket, 500 tickets to a show will be sold. He also knows that for every `\$1`

increase in price, 10 fewer tickets will be sold.

a) Model the revenue as a quartic function.

b) What ticket price will maximize revenue?

c) What is the maximum revenue?

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Q13

Prefer each radical multiplication and simplify where possible.

`3\sqrt{2}(2\sqrt{3} -3\sqrt{2})`

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Q14a

Prefer each radical multiplication and simplify where possible.

`(\sqrt{2} + x)(\sqrt{2} - x)`

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Q14b

For what value of `x`

is `\sqrt{x} + \sqrt{x} = \sqrt{x} \times \sqrt{x}`

, where `x > 0`

?
Justify your answer.

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Q15

Consider the quadratic function `f(x) = -\frac{1}{2}x^2 + 4x + 10`

.

a) Find the x-intercepts.

b) Use two methods to fid the vertex.

c) Sketch a graph of the function.

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Q16

A rectangle has a length that is `3`

m more than twice the width. If the total area is `65 m^2`

, find the dimensions of the rectangle.

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Q17

Find the equation, in standard form, of the quadratic function that has x-intercepts `-5 \pm \sqrt{3}`

and passes through the point `(-3, 8)`

.

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Q18

The graph of a quartic function is given

a) Find the equation of the function.

b) Find the maximum value of the function.

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Q19

Find the point(s) of intersection of `y = -x^2 + 5x + 8`

and `y= 2x- 10`

.

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Q20

a) Compare the graphs of `f(x) = 3x^2 -4`

and `g(x) = 3(x - 2)(x+ 2)`

b) What needs to be changed in the equation for `f(x)`

to make the tow functions part of the same family of curves with the same x-intercepts? Explain.

c) Describe the family of curves, in factored form, that has the same x-intercepts as `h(x) = 5x^2 -7`

.

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Q21

A baseball is travelling on a path given by the equation `y = -0.011x^2 + 1.15x + 1.22`

. The profile of the bleachers in the outfield can be modelled with the equation `y = 0.6x -72`

. All distances are in metres. Does the ball reach the bleachers for a home run? Justify your answer.

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Q22