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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Step-by-step explanation:
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