Question

Given the parent function f(x) = 2^x, which graph shows f(x) + 1?

a) exponential function going through point 0, 2 and ending up on the right
b) exponential function going through point 0, 0 and ending down on the right
c) exponential function going through point 0, 0 and ending up on the right
d) exponential function going through point 0, 1.5 and ending up on the right

Answer 1

Answer: First Option

a) exponential function going through point (0, 2) and ending up on the right

Explanation:

Look at the attached image, the red line represents a function of the form:

`f(x) = 2^x`

Note that this function cuts to the axis and at the point (0, 1)

Also when x tends to ∞ f(x) tends to ∞ and when f(x) tends to -∞ then f(x) tends to zero.

If we perform the transformation
`y = f(x) +1` then the graph of y is equal to the graph of f(x) displaced 1 unit up. Then the new cutting point with the axis y will be: (0, 2) as shown in the attached image (blue line)

The transform function is
`y =2^x +1`

Finally the answer is the first option