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○ c. {y|y ≠ } (use a comma to separate answers as needed.) ○ d. {y|y < …

$y=0$

Catégorie: calculus Mis à jour: 2026-02-09

Question

○ c. {y|y ≠ } (use a comma to separate answers as needed.)
○ d. {y|y < }
○ e. all real numbers

the 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 .
(type an equation.)

help me solve this view an example get n
review progress

Étapes de solution

  1. Understand the question

    ○ c. {y|y ≠ } (use a comma to separate answers as needed.)
    ○ d. {y|y < }
    ○ e. all real numbers

    the 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 .
    (type an equation.)

    help me solve this view an example get n
    review progress

  2. Explanation

    Step1: Recall exponential function properties

    For $f(x)=a \cdot b^x$ where $a>0, b>1$, the horizontal asymptote is the line that the function approaches but never touches as $x\to-\infty$.

    Step2: Evaluate limit as $x\to-\infty$

    $\lim_{x \to -\infty} 5 \cdot 8^x = 5 \cdot \lim_{x \to -\infty} 8^x = 5 \cdot 0 = 0$
    This means the function approaches $y=0$.

  3. Final answer

    $y=0$

Réponse

Explanation

Step1: Recall exponential function properties

For $f(x)=a \cdot b^x$ where $a>0, b>1$, the horizontal asymptote is the line that the function approaches but never touches as $x\to-\infty$.

Step2: Evaluate limit as $x\to-\infty$

$\lim_{x \to -\infty} 5 \cdot 8^x = 5 \cdot \lim_{x \to -\infty} 8^x = 5 \cdot 0 = 0$
This means the function approaches $y=0$.

Answer

$y=0$

Question Image

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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 2026-02-09T20:28:15

OCR Text

Show OCR extraction 
○ c. {y|y ≠ } (use a comma to separate answers as needed.)
○ d. {y|y < }
○ e. all real numbers

the 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 .
(type an equation.)

help me solve this  view an example  get n
review progress

Sujets liés

mathematicscalculusmultiple choice, calculationhigh schoolturns-1

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