Question

Consider the two functions given below.

f(x) = 3x + 4
g(x) = 2^x - 1

Which of the following pairs of transformations causes the graphs of the functions to have the same y-intercept?

f(x) - 3 and g(x) + 1

f(x) + 4 and g(x) - 1

f(x) - 2 and g(x) + 1

f(x) + 3 and g(x) - 6

Answer 1

This means which transformation makes the same answer at x = 0

f(x) = 3x + 4

`g(x) = {2}^(x) - 1`

f(0) = 4
g(0) = 1 - 1 = 0

Which transformation makes 4 = 0?

4 + x = 0 + y

4 - 3 =0 + 1

1 = 1

Option 1 is your answer

Answer 2

Option A is the correct answer.

Explanation:

y intercept means x value is 0.

f(0) = 3 x 0 + 4 = 4

`g(0)=2^0-1=1-1=0`

We need same y intercepts

That is f(0) = g(0)

4 + a = 0 + b

Checking all the options

a) f(x) - 3 and g(x) + 1

4 - 3 and 0 + 1

1 and 1

Option A is correct.

b) f(x) + 4 and g(x) - 1

4 + 4 and 0 - 1

8 and -1

Option B is wrong.

c) f(x) - 2 and g(x) + 1

4 - 2 and 0 + 1

2 and 1

Option C is wrong.

d) f(x) + 3 and g(x) - 6

4 + 3 and 0 - 6

7 and -6

Option D is wrong.

So, Option A is the correct answer.