which value of a in the exponential function below would cause the function to stretch?\n$f(x)=a(\\frac{1}{3}…
which value of a in the exponential function below would cause the function to stretch?\n$f(x)=a(\\frac{1}{3})^x$\n0.3\n0.9\n1.0\n1.5
Answer
Explanation:
Step1: Recall vertical - stretch rule
For an exponential function of the form $y = a\cdot b^x$, if $|a|> 1$, the graph of the function $y = b^x$ is vertically stretched.
Step2: Analyze each option
- For $a = 0.3$, since $|0.3|=0.3<1$, it causes a vertical compression.
- For $a = 0.9$, since $|0.9| = 0.9<1$, it causes a vertical compression.
- For $a = 1.0$, since $|1.0|=1$, there is no vertical stretch or compression.
- For $a = 1.5$, since $|1.5|>1$, it causes a vertical stretch.
Answer:
1.5