Chapter 1 to 3 Review Questions
Chapter
Chapter 3
Section
Chapter 1 to 3 Review Questions
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Solutions 40 Videos

Identify the relation that is not a function.

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Q1

For the graph of f(x) = \sqrt{x}, identify the transformation that would not be applied to f(x) to obtain the graph of y = 2f(-2x) + 3.

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Q2

An American visitor to Canada uses this function to convert from temperature in degrees Celsius into degrees Fahrenheit: f(x) = 2x+ 30.

a) f^{-1}(x) = \frac{x + 30}{2}

b) f^{-1}(x) = \frac{x - 30}{2}

c) f^{-1}(x) = \frac{x - 2}{30}

d) f^{-1}(x) = \frac{x + 2}{30}

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Q3

The range of f(x) = -|x -2| + 3 is

A. \{y\in \mathbb{R} \vert y \leq 3\}

B. \{y\in \mathbb{R} \vert y \geq 3\}

C. \{y\in \mathbb{R} \vert 2 \leq y \leq 3\}

D. \{y\in \mathbb{R} \vert 0 \leq y \leq 2\}

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Q4

Which pairs of functions are equivalent?

h(x) = (x + 6)(x + 3)(x-6) and b(x) = (x + 3)(x^2 -36)

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Q5i

Which pairs of functions are equivalent?

b(t) = (3t + 2)^3 and c(t) = 27t^3 +54t^2 + 36t + 8

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Q5ii

Which pairs of functions are equivalent?

h(t) = (4 -t)^3 and c(t) =(t -4)^3

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Q5iii

Which pairs of functions are equivalent?

f(x) = (x^2 - 4x) -(2x^2 + 2x - 4)-(x^2 +1)

\displaystyle b(x) = (2x-5)(2x-1)

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Q5iv

Which expression has the restrictions y \neq -1, 0, \frac{1}{2} on its variable?

a) \displaystyle \frac{3y}{y -2} \times \frac{4(y-2)}6y{}

b) \displaystyle \frac{5y(y + 3)}{4y} \times \frac{y -5}{y + 3}

c) \displaystyle \frac{3y + 1}{2y -1} \div \frac{3y(y + 1)}{2y -1}

d)\displaystyle \frac{10y}{y + 2} \div \frac{5}{2(y + 2)}

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Q6

Factor and simplify.

\displaystyle \frac{x^2 -5x + 5}{x^2 -1} \times \frac{x^2 -4x -5}{x^2 -4}

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Q7

Find the sum and simplify.

\displaystyle \frac{5x -6}{x + 1} + \frac{3x}{x -4}

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Q8

Given the quadratic function f(x) = 3x^2 -6x + 15, identify the coordinates of the vertex.

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Q9

When the equation of a quadratic function is in factored form, which feature is most easily determined?

a) y-intercept

b) x-intercept

c) vetex

d) maximum value

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Q10

The height, l), in metres, of a baseball after Bill hits it with a hat is described by the function h(t) = 0.8 +29.4t -4.9t^2, where tis the time in seconds after the ball is struck. What is the maximum height of the hall?

A. 4.9 m

B. 29.4

C. 44.9 m

D. 25 m

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Q11

It costs a bus company $225 to run a minibus on a ski trip, plus $30 per passenger. The bus has a seating for 22 passengers and the company charges $60 per far if the bus is full. For each empty seat, the company has to increase the ticket price b y $5. How many empty seats should the bus run with to maximize profit from this trip?

A. 8

B. 6

C. 10

D. 2

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Q12

Without drawing the graph identify the function that has two zeros.

A. n(x) = -x^2 -6x -9

B. m(x) = 4(x + 1)^2 + 0.5

C. f(x) = -5(x + 1.3)^2

D. g(x) = -2(x + 3.6)^2 + 4.1

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Q13

The graph of a function f(x) =x^2 -kx + k + 8 touches the x-axis at one point. What are the possible values of k?

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Q14

For f(x) = 2(x - 3)^2 + 5, x \geq 3, determine the equation for inverse.

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Q15

The relation that is also a function is

A. x^2 + y^2 = 25

B. y^2 =x

C. x^2 =y

D. x^2 - y^2 = 25

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Q16

Given f(x) = x^2 -5x + 3, then

A. f(-1) = -3

B. f(-1) = 7

C. f(-1) = -1

D. f(-1) = 9

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Q17

Which of the Following statements is not true?

a) The horizontal line test can be used to show that a relation is a function.

b) The set of all possible input values of a function is called the domain.

c) he equation y = 3x + 5 describes a function.

d) This set of ordered pairs describes a function:

\{(0, 1), (1, 2), (3, -3), (4, -1)\}

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Q18

Find the range of f(x) = \frac{3}{x}.

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Q19

Find the inverse of f(x) = 5x -7

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Q20

Find the inverse of g(x) =x^2 -5x- 6

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Q21

Which of the following statements is false?

a) The domain of f is the range of f^{-1}.

b) The graph of the inverse can be found by reflecting y =f(x) in the line y= x.

c) The domain of f^{-1} is the range of f.

d) To determine the equation of the inverse, interchange x and y and solve for x.

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Q22

If f(x) = 3(x+ 2)^2-5, the domain must be restricted to which interval if the inverse is to be a function?

a) x \geq -5

b) x \geq -2

c) x \geq 2

d) x \geq 5

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Q23

The inverse of f(x) = \sqrt{x -1} is

A. f^{-1}(x) = x^2 + 1, x \leq 0

B. f^{-1}(x) = x^2 - 1, x \leq 0

C. f^{-1}(x) = x^2 + 1, x \geq 0

D. f^{-1}(x) = x^2 - 1, x \leq 0

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Q24

What transformations are applied to y = f(x) to obtain the graph of y = af(x-p)+ q, if a< 0, p<0, and q< 0?

a) Vertical stretch by a factor of la|, followed by a translation |p| units to the left and |q| units down

b) Reflection in the x-axis, vertical stretch by a factor of |a|, followed by a translation |p| units to the right and |a| units down

c) Reflection in the x-axis, vertical stretch by a factor of |a|, following by a translation |p| units to the left and |q| units down.

d) Reflection in the x-axis, vertical stretch by a 6 factor of |a|, followed by a translation |p| units to the right and |q| units up

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Q25

Find the vertex of y = -2x^2 -12x -19.

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Q26

The coordinates of the vertex for the graph of y =(x + 2)(x -3) are

A. (-2, 3)

B. ( - \frac{1}{2}, -\frac{21}{4})

C. (2, 3)

D. (\frac{1}{2}, - \frac{25}{4})

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Q27

The profit function for a new product is given by P(x) = -4x^2 + 28x -40, where x is the number sold in thousands. How many items must be sold for the company to break even?

a) 2000 or 5000

b) 2000 or 3500

c) 5000 or 7000

d) 3500 or 7000

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Q28

Which of the following statements is not true for the equation of a quadratic function?

a) In standard form, they-intercept is clearly visible.

b) In vertex form, the break-even points are clearly visible.

c) In factored form, the x-intercepts are clearly visible.

d) In vertex form, the coordinates of the vertex are clearly visible.

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Q29

State the value of the discriminant, D, and the number of roots for 7x^2 + 12x + 6 =0.

A. D = 312, n =2

B. D = 24, n =2

C. D = 312, n =1

D. D = -24, n = 0

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Q30

The simplified form of \frac{7}{ab} - \frac{2}{b} + \frac{1}{3a^2} is

A. \displaystyle \frac{6}{ab -b + 3a^2}, a , b \neq 0

B. \displaystyle \frac{21a-6a^2 + b}{3a^2b}, a , b \neq 0

C. \displaystyle \frac{7a -2a^2 + b}{3a^2b}, a , b \neq 0

D. \displaystyle \frac{7a -2b + ab}{3a^3b^2}, a , b \neq 0

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Q31

Simplify

\displaystyle \frac{x^2 -4}{x + 3} \div \frac{2x + 4}{x^2 -9}

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Q32

For \displaystyle h(x) = 3x^2 -24x + 50

find

i. the domain and range.

ii. the relationship to the parent function. including all applied transformations

iii. a sketch of the function

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Q33a

For \displaystyle h(x) = 5 - 2\sqrt{3x + 6}

find

i. the domain and range.

ii. the relationship to the parent function. including all applied transformations

iii. a sketch of the function

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Q33b

For \displaystyle h(x) = \frac{1}{\frac{1}{3}(x -6)} -2

find

i. the domain and range.

ii. the relationship to the parent function. including all applied transformations

iii. a sketch of the function

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Q33c

Sacha and Jill set off at the same time on a 30 km walk for charity. Sacha, who has trained all year for this event, walks 1.4 km/h faster than Jill, but sees a friend on the route and stops to talk for 20 min. Even with this delay, Sacha finishes the walk 2 h ahead ofJill. How fast was each person walking, and how long did it take for each person to finish the walk?

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Q34

Jon is running a ski trip over March Break. Last year he had 25 students go and each paid $550. This year he will increase the price and knows that for each $50 price increase, 2 fewer students will go on the trip. The bus costs a flat fee of$5500, and hotel and lift tickets cost $240 per person. Determine

a) the number of students who must go for Josh to break even

b) the cost of the trip that will maximize his profit

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Q35