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=(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=(1)/(a^(\infty))+k,a>1 \\ \Rightarrow-4=k \end{gathered}`

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