Textbook

Functions 11 McGraw-Hill
Chapter

Chapter 1
Section

Practice Test for Functions and Quadratics

Purchase this Material for $5

You need to sign up or log in to purchase.

Subscribe for All Access
You need to sign up or log in to purchase.

Solutions
28 Videos

Is the following statement true or false?

- Every relation is a special type of function.

Buy to View

Q1a

Is the following statement true or false?

- Every function is a special type of relation.

Buy to View

Q1b

Is the following statement true or false?

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

can be any real number except`x = 2`

.

Buy to View

Q1c

Is the following statement true or false?

`\sqrt{81}`

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

.

Buy to View

Q1d

Is the following statement true or false?

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

Buy to View

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.

Buy to View

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}`

Buy to View

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

Buy to View

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}
```

Buy to View

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}
```

Buy to View

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\}`

Buy to View

Q7

State the domain and the range of each function.

Buy to View

Q8a

State the domain and the range of each function.

Buy to View

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.

Buy to View

Q9

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

Buy to View

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.

Buy to View

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?

Buy to View

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?

Buy to View

Q13

Prefer each radical multiplication and simplify where possible.

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

Buy to View

Q14a

Prefer each radical multiplication and simplify where possible.

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

Buy to View

Q14b

For what value of `x`

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

, where `x > 0`

?
Justify your answer.

Buy to View

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.

Buy to View

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.

Buy to View

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)`

.

Buy to View

Q18

The graph of a quartic function is given

a) Find the equation of the function.

b) Find the maximum value of the function.

Buy to View

Q19

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

and `y= 2x- 10`

.

Buy to View

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`

.

Buy to View

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.

Buy to View

Q22