1. For each of the given linear equation, draw the
graph, determine domain and range, intercepts,
intervals of increase or decrease and signs
of the functions:
a. f(x) = 2x - 4
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c. h(x) =
- 4x -5
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b. g(x) = (-1/5)
x + 3
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d. k(x) = (3/4)
x + 4
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2.
The table of values shown represents
a linear function:
x
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-6
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-3
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0
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9
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f(x)
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23
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14
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5
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-22
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a.
Determine the rule of
correspondence of this function.
b. What are the signs of this graph?
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3.
Cynthia charges an hourly rate
when she babysits. She receives $ 28,50 for 3 hours
and $ 47,50 for 5 hours.
a. What is her hourly rate?
b. Determine the rule of correspondence of this
linear function.
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4.
A 9 km trip by taxi costs $ 7,00
and a 24 km trip costs $ 14,50.
a. What is the initial charge as you get into this
taxi?
b. What is the rate per kilometre?
c. What is the rule of correspondence of this linear function?
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5.
For each of the given quadratic
functions, draw the graph, determine the vertex, domain and range,
axis of symmetry, intercepts, intervals of
increase or decrease and signs of the functions:
a. f(x) =
x2 - 9
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d. j(x) =
- (x - 3)2 - 7
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b. g(x) = x2 + 4
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e. k(x) = 3(x +
1)2 + 4
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c. h(x) =
- (x + 5)2
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f. p(x) = 1/4 (x -
3)2 - 9
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6.
Write each of the following quadratic equations in standard form
and determine the coordinates of the
vertex for each one.
a. f(x) = x2 + 6x
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d. k(x) =
4x2 - 16x + 8
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b. g(x) = 2x2 + 8x + 3
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e. p(x) =
- 0.5x2 + 4x - 3
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c. h(x) =
- 3x2 + 6x + 1
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f. q(x) =
3x2 + 30x +
2
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7.
Use the given table of values
to determine the rule of correspondence of each quadratic function.
Give your answers in standard form
and in general form:
a.
x
|
-5
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-4
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-2 |
-1
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0
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f(x)
|
17
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7
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-1
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1
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7
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b.
x
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-6
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-4
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-2 |
-1
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0
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i(x)
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34
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46
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34
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19
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-2
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8.
What are the x-intercepts
of each
of the following quadratic
functions?
a. F(x) = 2x2 - 3x + 1
b. G(x) = 2(x -
1)2 - 18
c. H(x) = 6x2 + 7x - 3 |
d. K(x) = 9x2 - 3x - 30
e.
P(x) = x2 - 5x + 4
f.
Q(x) = 4(x2 - 2,25)
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9. Determine what each of the following families of
parabolas have in common:
y1 = x2 - 6x + 11
y2 = 2x2 - 4x + 4
y3 = ½ x2 + 4x + 10 |
y1 = 2x2 + 12x + 14
y2 = ½ x2 + 3x +
½
y3 = - 3x2 - 18x - 31
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y1 = 4x2 - 16x + 23
y2 = 0,5x2 - 2x + 5
y3 = 2x2 - 8x + 3
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10.
Triangle ABC has a base represented by the expression
(2x - 3) cm and a height
represented by (x + 4) cm.
What are the numerical
values of these dimensions when
the area of this triangle
measures 3 cm2 ?
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11.
A rectangular park measuring 25 m by 30 m is surrounded by
a path (shaded
part) of constant width (x) metres.
If the area of
this path is 174 m2, what is the
numerical value of its width ?
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Extra-Review #2
Find the equation for each linear function described below:
A.
1. Slope 2/5 and x-intercept 4.
2. Slope -1 and y-intercept 13.
3. X-intercept 6 and y-intercept -2.
4. Slope - 2/3 and x-intercept 0.
5. Going through points A (3, -2) and B ( -1, 4).
6. Going through points C (-4, 1) and D (-5, 3).
7. Going through points E (-2, 5) and F ( -1, 6).
8. Going through points G (-3, -5) and H ( 1, 7).
9. Going through points I (0, -2) and J ( -1, 0).
10. Going through points A (4, -6) and B ( 7, 3).
B.
1. Parallel to the line 3x - y + 1 = 0 and going
through
point A (-3, 4).
2. Perpendicular to the line 4x - 2y + 7 = 0 and
going
through point A (4, 4).
3. Parallel to the line 5x - 2y + 3 = 0 and going
through
point A (-4, 2).
4. Parallel to the line 4x + y - 12 = 0 and going
through
point A (3, -4).
5. Perpendicular to the line 2x - y - 6 = 0 and going
through
point A (2, 6).
6. Parallel to the line 2x - y + 3 = 0 and going
through
point A (0, -4).
7. Perpendicular to the line 4x + y - 3 = 0 and going
through
point A (0, 4).
8. Perpendicular to the line 3x + 2y + 5 = 0 and
going
through point A (5, -6).
9. Parallel to the line x - 4y - 7 = 0 and going
through
point A (-4, 3).
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Extra-Review ER4 Linear and Quadratic Functions