What transformations are applied to the graph of the function f(x) = 10^x to produce the graph of the function g(x) = 3(10)^x -
2 ?
A.
a vertical dilation by a factor of and a horizontal shift to the right 2 units
B.
a vertical dilation by a factor of and a vertical shift down 2 units
C.
a vertical dilation by a factor of 3 and a vertical shift down 2 units
D.
a vertical dilation by a factor of 3 and a horizontal shift to the right 2 units
A.
a vertical dilation by a factor of and a horizontal shift to the right 2 units
B.
a vertical dilation by a factor of and a vertical shift down 2 units
C.
a vertical dilation by a factor of 3 and a vertical shift down 2 units
D.
a vertical dilation by a factor of 3 and a horizontal shift to the right 2 units
2 answers:
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Answer (numbers needed in boxes, going from top to bottom):
1
-1
-3
3
Step-by-step explanation:
f(x) is another way of saying y. So, the table is asking, "when substituting these x values for the x's in the function, what does y equal?" So, to answer the question, substitute each x value into the equation and solve.
1) Start with the x value of 1. Substitute 1 for x in y = 2x - 1 and solve:
So, when x equals 1, y equals 1. Therefore, the first box on the top must be filled out with the number 1.
2) Do the same with the rest of the x values. Here are the steps to solve each one, going in order from the top towards the bottom:
x = 0
x = -1
x = 2