which of the following statements is not true for the graph of f(x)=e^x? choose the statement that is not…
which of the following statements is not true for the graph of f(x)=e^x? choose the statement that is not true below. a. the line y = 0 is a horizontal asymptote. b. the graph of f(x)=e^x lies between the graphs of y = 3^x and y = 4^x. c. the graph of f(x)=e^x approaches 0 as x approaches negative infinity. d. the graph of f(x)=e^x intersects the y - axis at (0,1).
Answer
Explanation:
Step1: Analyze option A
As $x\to-\infty$, $e^{x}\to0$, so $y = 0$ is a horizontal - asymptote. This statement is true.
Step2: Analyze option B
The function $y = e^{x}$ where $e\approx2.718$. Since $2.718<3$, the graph of $y = e^{x}$ does not lie between the graphs of $y = 3^{x}$ and $y = 4^{x}$. This statement is false.
Step3: Analyze option C
As $x\to-\infty$, $e^{x}\to0$. This statement is true.
Step4: Analyze option D
When $x = 0$, $f(0)=e^{0}=1$, so the graph of $y = e^{x}$ intersects the $y$-axis at $(0,1)$. This statement is true.
Answer:
B. The graph of $f(x)=e^{x}$ lies between the graphs of $y = 3^{x}$ and $y = 4^{x}$.