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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

Respuesta :

luisejr77

Answer: First Option

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

Step-by-step explanation:

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

[tex]f(x) = 2^x[/tex]

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 [tex]y = f(x) +1[/tex] 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 [tex]y =2^x +1[/tex]

Finally the answer is the first option

Ver imagen luisejr77

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