HELP TEST DUE 12/1 The function f(x) = x − 1 is changed to f(x) = 1 4 x − 1. Which describes the effect of the change on the gra
ph of the original function?
A) The line will be steeper.
B) The line will be less steep.
C) Line changes from increasing to decreasing.
D) Line changes from decreasing to increasing.
2) Sketch the linear function f(x) = 1 6 (3x + 1). Which key feature of the graph is true?
A) y-intercept (0, 1)
B) x-intercept ( 1 6 , 0)
C) x-intercept (− 1 3 , 0)
D) y-intercept (0, − 1 6 )
3) The graph of the line y = 4 is a
A) vertical line with a slope of zero.
B) horizontal line with a slope of zero.
C) vertical line with an undefined slope.
D) horizontal line with an undefined slope.
4) The function f(x) = −2x + 5 is changed to f(x) = 2x + 5. Which describes the effect of the change on the graph of the original function?
A) The line will be steeper.
B) The line will be less steep.
C) Line changes from increasing to decreasing.
D) Line changes from decreasing to increasing.
5) x y
0 1
1 2
2 3
3 4
4 5
Which graph represents the function described in the table?
A) A
B) B
C) C
D) D
6) The graph of f(x) = x is given. Which graph represents g(x) = 1 3 x?
A) A
B) B
C) C
D) D
7) Mike opens a checking account with an initial deposit of $200. Without making additional deposits, he withdraws $25 each week. Kyle also opens a checking account. The function y = 25x + 200 represents the current balance in Kyle's account. Suppose the linear functions representing the two situations are graphed on a coordinate plane. Which statement BEST describes the graphs of the functions?
A) The rate of change is the same, but the y-intercepts are different.
B) Both the rate of change and the y-intercepts are the same.
C) The rate of change is different, but the y-intercepts are the same.
D) Both the rate of change and the y-intercepts are different.
8) What is the effect on the graph of the parent function f(x) = x when f(x) is replaced with f(x - 7)?
A) shifts the line 7 units up
B) shifts the line 7 units down
C) increases the slope of the line by a factor of 7
D) decreases the slope of the line by a factor of 7
9) Which function is represented by the graph?
A) f(x) = 2x + 6
B) f(x) = -2x + 6
C) f(x) = 1 2 x + 6
D) f(x) = - 1 2 x + 6
10) The graph of f(x) = x is given. Which equation will translate the graph 3 units down?
A) g(x) = 3x
B) g(x) = -3x
C) g(x) = x - 3
D) g(x) = x + 3
A) The line will be steeper.
B) The line will be less steep.
C) Line changes from increasing to decreasing.
D) Line changes from decreasing to increasing.
2) Sketch the linear function f(x) = 1 6 (3x + 1). Which key feature of the graph is true?
A) y-intercept (0, 1)
B) x-intercept ( 1 6 , 0)
C) x-intercept (− 1 3 , 0)
D) y-intercept (0, − 1 6 )
3) The graph of the line y = 4 is a
A) vertical line with a slope of zero.
B) horizontal line with a slope of zero.
C) vertical line with an undefined slope.
D) horizontal line with an undefined slope.
4) The function f(x) = −2x + 5 is changed to f(x) = 2x + 5. Which describes the effect of the change on the graph of the original function?
A) The line will be steeper.
B) The line will be less steep.
C) Line changes from increasing to decreasing.
D) Line changes from decreasing to increasing.
5) x y
0 1
1 2
2 3
3 4
4 5
Which graph represents the function described in the table?
A) A
B) B
C) C
D) D
6) The graph of f(x) = x is given. Which graph represents g(x) = 1 3 x?
A) A
B) B
C) C
D) D
7) Mike opens a checking account with an initial deposit of $200. Without making additional deposits, he withdraws $25 each week. Kyle also opens a checking account. The function y = 25x + 200 represents the current balance in Kyle's account. Suppose the linear functions representing the two situations are graphed on a coordinate plane. Which statement BEST describes the graphs of the functions?
A) The rate of change is the same, but the y-intercepts are different.
B) Both the rate of change and the y-intercepts are the same.
C) The rate of change is different, but the y-intercepts are the same.
D) Both the rate of change and the y-intercepts are different.
8) What is the effect on the graph of the parent function f(x) = x when f(x) is replaced with f(x - 7)?
A) shifts the line 7 units up
B) shifts the line 7 units down
C) increases the slope of the line by a factor of 7
D) decreases the slope of the line by a factor of 7
9) Which function is represented by the graph?
A) f(x) = 2x + 6
B) f(x) = -2x + 6
C) f(x) = 1 2 x + 6
D) f(x) = - 1 2 x + 6
10) The graph of f(x) = x is given. Which equation will translate the graph 3 units down?
A) g(x) = 3x
B) g(x) = -3x
C) g(x) = x - 3
D) g(x) = x + 3
2 answers:
Answer:
1. f(x) = 1/4x − 1. B) The line will be less steep. The slope is lower now
2. C)x-intercept (−1/3 , 0). Replacing f(x) = 0 we get x = -1/3
3. B)horizontal line with a slope of zero. The slope is 0 because there is no x in the equation.
4. D)Line changes from decreasing to increasing. The slope changed from negative to positive.
5. See first graph attached
6. See second graph attached. g(x) = (1/3)*x
7. C)The rate of change is different, but the y-intercepts are the same. The rate of change of Mike is negative because he withdraws $25 each week. The y-intercepts of Mike is $200 because that was his initial deposit.
8. B)shifts the line 7 units down. f(x-7) translates f(x) 7 units to the right, given the slope is positive ( = 1) then f(x) is translated 7 units down.
9. No graph is shown
10. C)g(x) = x - 3. g(x) = f(x) - 3, so g(x) is f(x) translated 3 units down.
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Answer:
a) $161.8
b i) Approximately 327.7 hours
ii) The cost of saving is less but the opportunity cost of saving can be higher with regards to technology and regulation
Step-by-step explanation:
The amount Mary would like to save, FV = $10,000
The time Mary over which Mary intends to save the amount, t = 5 years
Therefore, the number of monthly payments, n = 12
a) The amount in interest the bank pays compounding, i = 1.2% per annum
The amount that Mary will deposit each month is given as follows;
The compound interest formula is given as follows;
Where;
PMT = The monthly payment
Therefore, we get;
PMT = 10,000/((1 + 0.012/12)^(60) - 1)/(0.012/12)) ≈ 161.8
The amount she needs to deposit monthly, PMT ≈ $161.8
b i) Given that the minimum wage varies and we have a minimum wage here is officially approximately $79, which is 160 hours a month work
The number of hours work needed = 161.8/79 × 160 ≈ 327.7 hours a month approximately
b ii) Given that the interest rate for saving is lower than the interest rate for borrowing, the amount paid by saving is much lesser than the amount paid back when borrowing, therefore, it is more cost effective to save
However, while saving, changes may take place, such as the use of what is being saved for, therefore, it can be more beneficial to borrow and make use of the items now while they are still available and acceptable, such as the drive towards net zero is making fuel based cars less popular with the drive being towards electric cars.