Question

The functions f(x) and g(x) are described using the following equation and table:

f(x) = 4(1.02)x

x g(x)
-1 -4
0 6
1 8
2 10
Which statement best compares the y-intercepts of f(x) and g(x)?

Answer 1

Answer: OPTION D.

Step-by-step explanation:

The missing statements are:

A. The y-intercept of f(x) is equal to the y-intercept of g(x).

B. The y-intercept of f(x) is equal to 2 times the y-intercept of g(x).

C. The y-intercept of g(x) is equal to 2 times the y intercept of g(x)

D. The y intercept of g(x) is equal to 2 plus the y intercept of f(x).

It is important to remember that, by definition, the graph of a function intersects the y-axis when the value of "x" is zero ($x=0$).

So, given the table of the function g(x), you can observe that when $x=0$, the output value is:

$g(0)=6$

Therefore, you can determine that the graph of the function g(x) intersects the y-axis at  $y=6$

Now, given the following function f(x):

 $f(x) = 4(1.02)^x$

You need to substitute $x=0$ into the function f(x) and then evaluate, in order to find the y-intercept.

Then, you get that this is:

$f(0) = 4(1.02)^0\\\\f(0)=4(1)\\\\f(0)=4$

Therefore, based on this you can conclude that  the y-intercept of g(x) is equal to 2 plus the y-intercept of f(x).

Answer 2

Answer: D

Step-by-step explanation:

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