Question

If this is the graph of f(x)=a^(x+h)+k, then:

a.k > 1
b.a < 0
c.a > 1
d.0 < a < 1

Answer 1

C

Step-by-step explanation: The standard form of an exponential equation is

`a^(x+h) +k`

where a is the vertical dilation, h is the horinzontial translation, and k is the vertical translation.

Lets go through these options step by step.

A. In an exponetial equation, when k>1, the graph is translated upwards vertically. However, k could still be positive and doesn't be the shape of the picture of the graph always.

Plus our exponential function has an horinzontial asymptote at y=-4 so k here is negative, not positive.

B. When a<0, the graph end behavior changes. When a>1, the right side of the graph approaches infinity while the left side approaches an asymptote. However, when a<0, the graph could be two things. One ( when a< -1) could be that the right side approaches negative infinity, and the left side approaches asymptote. The other could be that (when -1<a<0) that the right side approaches an asymptote and the left side approaches negative infinity. In this function, this models a traditional exponetial function, when a is greater than 1 so B/D is Wrong.

C is correct, when a>1, the end behavior for the right side is infinity, and for the left side is some asymptote.