Question

-7 -6 -5 -4 -3 -2 ONO MN ++ HA -6-5-4-3-2-1 + 11 2 3 4 5 6 7 8 9 -2 -3 F-4 -5 -6 -7 -A + jo voo Alcon ixth If this is the graph of f(-x) = a +k, then : A. 0 < a < 1 B. a < 0 O c. a> 1 O D. K> 1

Answer 1

The function is

$f(x)=a^{(x+h)}+k$

The limit when x->+/- infinite are (analitically)

$\begin{gathered} \lim _{x\to\infty}f(x)=a^{(\infty+h)}+k=a^{\infty}+k \\ \text{and} \\ \lim _{x\to-\infty}f(x)=a^{(-\infty+h)}+k=\frac{1}{a^{\infty}}+k \\ \end{gathered}$

And, from the figure,

$\begin{gathered} \lim _{x\to\infty}f(x)=\infty \\ \text{and} \\ \lim _{x\to-\infty}f(x)=-4 \end{gathered}$

Therefore,

$\begin{gathered} \Rightarrow a^{\infty}+k=\infty \\ \Rightarrow a>1 \\ \text{and} \\ \Rightarrow-4=\frac{1}{a^{\infty}}+k,a>1 \\ \Rightarrow-4=k \end{gathered}$

Therefore, the answer is option C, a>1.