Question

Consider the function f (x) = 2x - 1

What is the output if the input is x - -3?
f (x) = __
Which is an ordered pair of the relation y = 2/3 x - 5?
A. (9, 2)
B. (6, -1)
C. (3, 3)
D. (-3, 7)
Which are examples of non-linear functions? Choose all that apply.(2 points)
A. y = 10x + 3
B. y = -3x + 6
C. y = 5x^3 + 5
D. y = 3x^2 + 10
E. y = 4x - 5
Determine the rate change of the linear function given the table below.
x. -3, -2, -1, 0, 1
y. -10, -7, -4, -1, 2
M = __
A computer technician charges a fee of $50 to diagnose a problem and $70 per hour to fix it. Write an equation in slope-intercept form to represent this situation. Identify the initial value and the rate of change.
A. The rate of change is $120.
B. The initial value is $50 and the rate of change is $70.
C. The initial value is $120.
D. The initial value if $70 and the rate of change is $50.
Which equation of the linear function models the relationship shown in the table.
X. 2, 4, 5, 8, 10.
Y. 21, 17, 15, 9, 5.
A. y=−3x+19
B. y = 2x + 21
C. y = 2x + 24
D. y = -2x + 25
Part A
What is the common difference of the arithmetic sequence 50, 46, 42, 38,....?
A. -4
B. -3
C. 4
D. 2
Part B.
Determine the 6th and 20th terms of the arithmetic sequence above.
6th term is __
20th term is __

Answer 1

[AI-generated answer — Bot GPT 3.5]

Part A

What is the output if the input is x = -3?
f(x) = 2(-3) - 1 = -6 - 1 = -7
Therefore, the output is -7.

Which is an ordered pair of the relation y = 2/3x - 5?
Plug in the given x-values into the equation to find the corresponding y-value:
A. (9, 2) - y = 2/3(9) - 5 = 6 - 5 = 1
B. (6, -1) - y = 2/3(6) - 5 = 4 - 5 = -1
C. (3, 3) - y = 2/3(3) - 5 = 2 - 5 = -3
D. (-3, 7) - y = 2/3(-3) - 5 = -2 - 5 = -7
Therefore, the correct answer is B. (6, -1).

Which are examples of non-linear functions?
Non-linear functions are C. y = 5x^3 + 5 and D. y = 3x^2 + 10.

Determine the rate change of the linear function given the table below.
Calculate the rate of change by finding the difference in y-values and dividing by the difference in x-values:
Rate of change (M) = (2 - (-10))/(1 - (-3)) = 12/4 = 3
Therefore, the rate change is 3.

A computer technician charges a fee of $50 to diagnose a problem and $70 per hour to fix it. Write an equation in slope-intercept form to represent this situation.
Let x be the number of hours and y be the total cost. The equation is: y = 70x + 50
The initial value is $50 and the rate of change is $70.

Which equation of the linear function models the relationship shown in the table?
Plug in the given x-values into the equation to find the corresponding y-values for each option:
A. y = -3(2) + 19 = 13
B. y = 2(2) + 21 = 25
C. y = 2(2) + 24 = 28
D. y = -2(2) + 25 = 21
Therefore, the correct answer is B. y = 2x + 21.

Part A
What is the common difference of the arithmetic sequence 50, 46, 42, 38,....?
The common difference is -4.

Part B
Determine the 6th and 20th terms of the arithmetic sequence.
Find the general formula for the arithmetic sequence: An = 50 - 4(n-1)
6th term: A6 = 50 - 4(6-1) = 50 - 4(5) = 50 - 20 = 30
20th term: A20 = 50 - 4(20-1) = 50 - 4(19) = 50 - 76 = -26
Therefore, the 6th term is 30 and the 20th term is -26.