Practice Test for Functions and Quadratics
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Chapter 1
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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