Questions: Use transformations to graph the function. Determine the domain, range, horizontal asymptote, and y-intercept of the function. f(x)=6^(x-2) Use the graphing tool to graph the function. (For any answer boxes shown with the grapher, type an exact answer.) What is the domain of f(x)=6^(x-2) ? (-∞, ∞) (Type your answer in interval notation.) What is the range of f(x)=6^(x-2) ? (0, ∞) (Type your answer in interval notation.) Determine the horizontal asymptote of f(x)=6^(x-2). Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one horizontal asymptote, y=0. (Type an equation.) B. The function has two horizontal asymptotes. The top asymptote is and the bottom asymptote is (Type equations.) C. The function has no horizontal asymptotes. What is the y-intercept of f(x)=6^(x-2) ? (Type an integer or a simplified fraction.)

Use transformations to graph the function. Determine the domain, range, horizontal asymptote, and y-intercept of the function. f(x)=6^(x-2) Use the graphing tool to graph the function. (For any answer boxes shown with the grapher, type an exact answer.) What is the domain of f(x)=6^(x-2) ? (-∞, ∞) (Type your answer in interval notation.) What is the range of f(x)=6^(x-2) ? (0, ∞) (Type your answer in interval notation.) Determine the horizontal asymptote of f(x)=6^(x-2). Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one horizontal asymptote, y=0. (Type an equation.) B. The function has two horizontal asymptotes. The top asymptote is and the bottom asymptote is (Type equations.) C. The function has no horizontal asymptotes. What is the y-intercept of f(x)=6^(x-2) ? (Type an integer or a simplified fraction.)
Transcript text: Use transformations to graph the function. Determine the domain, range, horizontal asymptote, and $y$-intercept of the function. \[ f(x)=6^{x-2} \] Use the graphing tool to graph the function. $\square$ (For any answer boxes shown with the grapher, type an exact answer.) What is the domain of $f(x)=6^{x-2}$ ? \[ (-\infty, \infty) \] (Type your answer in interval notation.) What is the range of $f(x)=6^{x-2}$ ? $(0, \infty)$ (Type your answer in interval notation.) Determine the horizontal asymptote of $f(x)=6^{x-2}$. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one horizontal asymptote, $y=0$. (Type an equation.) B. The function has two horizontal asymptotes. The top asymptote is $\square$ and the bottom asymptote is $\square$ (Type equations.) C. The function has no horizontal asymptotes. What is the $y$-intercept of $f(x)=6^{x-2}$ ? $\square$ (Type an integer or a simplified fraction.)
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Solution

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Solution Steps

Step 1: Determine the Domain

The domain of the function \( f(x) = 6^{x-2} \) is all real numbers because there are no restrictions on the values that \( x \) can take for an exponential function.

Final Answer

The domain is \( (-\infty, \infty) \).

Step 2: Determine the Range

The range of the function \( f(x) = 6^{x-2} \) is all positive real numbers because an exponential function with a positive base never reaches zero or negative values.

Final Answer

The range is \( (0, \infty) \).

Step 3: Determine the Horizontal Asymptote

For the function \( f(x) = 6^{x-2} \), as \( x \) approaches negative infinity, \( 6^{x-2} \) approaches zero. Therefore, the horizontal asymptote is \( y = 0 \).

Final Answer

The horizontal asymptote is \( y = 0 \).

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