Problem 1 :
Which answer choice describes how the graph of f(x) = x^{2} was transformed to create the graph of n(x) = x^{2} – 1 ?
A) A vertical shift up B) A horizontal shift to the left
C) A vertical shift down D) A horizontal shift to the right
Solution :
A vertical shift down.
So, option C) is correct.
Problem 2 :
The expression d^{2} – d – 6 can be written in factored form as (d + 2) (d + k), where k represents a number. What is the value of k ? Record your answer and fill in the bubbles on your answer document.
Solution :
Given, the expression is d^{2} – d – 6
Factored form of above quadratic function is,
(d - 3) (d + 2)
k = -3
So, the value of k is -3.
Problem 3 :
The graph of a linear function is shown on the grid.
Which equation is best represented by this graph ?
A) y = (-7/4)x + 4 C) y = (-4/7)x + 4 |
B) y = (-7/4)x + 7 D) y = (-4/7)x + 7 |
Solution :
Slope (m) = -7/4
y - intercept (b) = 7
y = mx + b
y = -(7/4)x + 7
So, option B) is correct.
Problem 4 :
Which expression is equivalent to (c^{8}(d^{6})^{3})/c^{2} for all values of c for which the expression is defined ?
F) c^{4}d^{9 }G) c^{4}d^{18 }H) c^{6}d^{9 }J) c^{6}d^{18}
Solution :
(c^{8}(d^{6})^{3})/c^{2}
(c^{8}(d^{18}))/c^{2}
c^{6}d^{18}
So, option J) is correct.
Problem 5 :
Which value of x is the solution to this equation ?
5x^{2} = 30x – 45
A) x = 3 B) x = -3 C) x = 5 D) x = -5
Solution :
5x^{2} = 30x – 45
5x^{2} - 30x + 45 = 0
a = 5, b = -30, c = 45
So, the value of x is 3.
Hence, option A) is correct.
Problem 6 :
A florist is making bouquets of flowers for a wedding. Each bouquet will have 9 flowers. The graph shows the linear relationship between y, the number of flowers used, and x, the number of bouquets.
The florist will use no more than 8 bouquets for the wedding. Which set best represents the domain of the function for this situation ?
F) {0, 2, 4, 6, 8, 10}
G) {0, 1, 2, 3, 4, 5, 6, 7, 8}
H) {0, 18, 36, 54, 72, 90}
J) {0, 9, 18, 27, 36, 45, 54, 63, 72}
Solution :
Domain is all the possible x values of the function.
0 ≤ x ≤ 8
{0, 1, 2, 3, 4, 5, 6, 7, 8}
So, option G) is correct.
Problem 7 :
The graph of a line is shown on the grid. The coordinates of both points indicated on the graph of the line are integers.
What is the rate of change of y with respect to x for this line ?
A) 5/2 B) -6/5 C) 2/3 D) -5/6
Solution :
m = (y_{2} - y_{1})/(x_{2} - x_{1})
(x_{1}, y_{1}) = (-3, 5)
(x_{2}, y_{2}) = (9, -5)
m = (-5 - 5)/(9 + 3)
= -10/12
m = -5/6
So, option D) is correct.
Problem 8 :
What is the value of the y – intercept of the graph of h(x) = 12.3(4.9)^{x} ? Record your answer and fill in the bubbles on your answer document.
Solution :
h(x) = 12.3(4.9)^{x}
To find y - intercept :
x = 0
h(0) = 12.3(4.9)^{0}
h(0) = 12.3
Problem 9 :
Which expression is equivalent to (8.8 × 10^{9})/(2.2 × 10^{-3})
A) 4 × 10^{12 }B) 4 × 10^{6 }C) 4 × 10^{-3 }D) 4 × 10^{-6}
Solution :
8.8 = 4 × 2.2
= 4 × 10^{ (9 + 3)}
= 4 × 10^{12}
So, option A) is correct.
Problem 10 :
A person dives into a pool from its edge to swim to the other side. The table shows the depth in feet of the person from the surface of the water after x seconds. The data can be modeled by a quadratic function.
Pool
Which function best models the data ?
F) d(x) = 0.05x^{2} + 0.74x
G) d(x) = 0.05x^{2} + 0.74x + 9.17
H) d(x) = 0.26x^{2} - 3.11x
J) d(x) = 0.26x^{2} - 3.11x + 1
Solution :
Quadratic function d(x) = ax^{2} + bx + c
From the table, let us take first 3 values to get the equation.
x = 1 ==> y = -2.85
x = 4 ==> y = -8,28
x = 6 ==> y = -9.3
Now, the equations becomes,
a + b + c = -2.85 --- (1)
16a + 4b + c = -8.28 --- (2)
36a + 6b + c = -9.3 --- (3)
Solving (1) and (2) we get,
-15a - 3b = 5.43
Dividing -3 on each sides.
5a + b = -1.81 --- (4)
Solving (3) and (1) we get,
35a + 5b = -6.45
Dividing 5 on each sides.
7a + b = -0.52 --- (5)
Solving (4) and (5) we get,
-2a = -0.52
a = 0.52/2
a = 0.26
a = 0.26 substitute the equation (4).
5(0.26) + b = -1.81
1.3 = b = -1.81
b = -1.81 - 1.3
b = -3.11
a = 0.26 and b = -3.11 substitute the equation (1).
0.26 - 3.11 + c = -2.85
-2.85 + c = -2.85
c = -2.85 + 2.85
c = 0
a = 0.26, b = -3.11 and c = 0 substitute the quadratic function.
d(x) = 0.26x^{2} - 3.11x
So, option H) is correct.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM