2025rs2-red mountain-campos-honors algebra ii (lms)< 6.1 hw (ha2) (lms …

Question

2025rs2-red mountain-campos-honors algebra ii (lms)< 6.1 hw (ha2) (lms graded)part 5 of 5identify the domain, range, intercept, and asymptote of the exponential function. then describe the end behavior.$f(x)=5\\cdot8^{x}$○ d. $\\{y|y < \\ \\}$○ e. all real numbersthe y-intercept of the function $f(x)=5\\cdot8^{x}$ is 5.(type an integer or a decimal.)the asymptote of $f(x)=5\\cdot8^{x}$ is $y=0$.(type an equation.)as x approaches $-\\infty$, the values of f(x) approach $\\square$, and as x approaches $\\infty$, the values of f(x) approach $\\square$.

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2025rs2-red mountain-campos-honors algebra ii (lms)< 6.1 hw (ha2) (lms graded)part 5 of 5identify the domain, range, intercept, and asymptote of the exponential function. then describe the end behavior.$f(x)=5\\cdot8^{x}$○ d. $\\{y|y < \\ \\}$○ e. all real numbersthe y-intercept of the function $f(x)=5\\cdot8^{x}$ is 5.(type an integer or a decimal.)the asymptote of $f(x)=5\\cdot8^{x}$ is $y=0$.(type an equation.)as x approaches $-\\infty$, the values of f(x) approach $\\square$, and as x approaches $\\infty$, the values of f(x) approach $\\square$.
Explanation
Step1: Find the domain

Exponential functions accept all real $x$.
Domain: $(-\infty, \infty)$ (all real numbers)

Step2: Find the range

$8^x > 0$ for all $x$, so $5 \cdot 8^x > 0$.
Range: $\{y | y > 0\}$

Step3: Confirm y-intercept

Set $x=0$: $f(0)=5 \cdot 8^0 = 5 \cdot 1 = 5$

Step4: Identify asymptote

As $x \to -\infty$, $8^x \to 0$, so $f(x) \to 0$; horizontal asymptote $y=0$

Step5: Describe end behavior

As $x \to -\infty$: $8^x \to 0$, so $f(x) \to 0$
As $x \to \infty$: $8^x \to \infty$, so $f(x) \to \infty$
Final answer
Domain: All real numbers
Range: $\{y | y > 0\}$
y-intercept: 5
Asymptote: $y=0$
End behavior: As $x \to -\infty$, $f(x) \to 0$; As $x \to \infty$, $f(x) \to \infty$

Answer

Domain: All real numbers
Range: $\{y | y > 0\}$
y-intercept: 5
Asymptote: $y=0$
End behavior: As $x \to -\infty$, $f(x) \to 0$; As $x \to \infty$, $f(x) \to \infty$

Explanation

Step1: Find the domain

Exponential functions accept all real $x$.
Domain: $(-\infty, \infty)$ (all real numbers)

Step2: Find the range

$8^x > 0$ for all $x$, so $5 \cdot 8^x > 0$.
Range: $\{y | y > 0\}$

Step3: Confirm y-intercept

Set $x=0$: $f(0)=5 \cdot 8^0 = 5 \cdot 1 = 5$

Step4: Identify asymptote

As $x \to -\infty$, $8^x \to 0$, so $f(x) \to 0$; horizontal asymptote $y=0$

Step5: Describe end behavior

As $x \to -\infty$: $8^x \to 0$, so $f(x) \to 0$
As $x \to \infty$: $8^x \to \infty$, so $f(x) \to \infty$

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Question Analysis

Subject mathematics

Sub Subject calculus

Education Level high school

Difficulty unspecified

Question Type multiple choice, calculation

Multi Question No

Question Count 1

Analysis Status completed

Analyzed At 2026-02-09T20:30:37

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2025rs2-red mountain-campos-honors algebra ii (lms)< 6.1 hw (ha2) (lms graded)part 5 of 5identify the domain, range, intercept, and asymptote of the exponential function. then describe the end behavior.$f(x)=5\\cdot8^{x}$○ d. $\\{y|y < \\ \\}$○ e. all real numbersthe y-intercept of the function $f(x)=5\\cdot8^{x}$ is 5.(type an integer or a decimal.)the asymptote of $f(x)=5\\cdot8^{x}$ is $y=0$.(type an equation.)as x approaches $-\\infty$, the values of f(x) approach $\\square$, and as x approaches $\\infty$, the values of f(x) approach $\\square$.

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