Question

The graphs of two exponential functions, f and g, are shown on the coordinate plane below.

If g(x) = f(x) + k, what is the value of k?

A. -6
B. 6
C. 7
D. -7

Answer 1

option c

Explanation:

Answer 2

C. 7

Explanation:

We have been given graphs of two exponential functions, f and g.

`g(x)=f(x)+k`

We can see that our parent function f(x) is translated k units to get function g(x).

The rules for translation are mentioned below.

Horizontal shifting:

`f(x-a)`= Graph shifted to right by a units.

`f(x+a)`= Graph shifted to left by a units.

Vertical shifting:

`f(x)+a`= Graph shifted upwards by a units.

`f(x)-a`= Graph shifted downwards by a units.

Upon comparing our given graph with transformation rules we can see that our function f(x) is translated k units upward to get function g(x).

Now let us find the value of k from our given graph.

We can see that initial value (y-intercept) of f(x) is -4 and initial value of g(x) is 3. Difference between y-intercepts of both functions is 7.

`\text{Difference between y-intercepts}= 3--4=3+4=7`

Our parent function f(x) is shifted 7 units upwards to get new function g(x), therefore the value of k is 7 and option C is the correct choice.