select the correct answer.

which exponential function has an x-intercept?

$ f(x) = 100^{x-5} - 1 $

$ f(x) = 3^{x-4} + 2 $

$ f(x) = 7^{x-1} + 1 $

$ f(x) = -8^{x+1} - 3 $

Question

select the correct answer.

which exponential function has an x-intercept?

$ f(x) = 100^{x-5} - 1 $

$ f(x) = 3^{x-4} + 2 $

$ f(x) = 7^{x-1} + 1 $

$ f(x) = -8^{x+1} - 3 $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponential Functions" ], "new_concepts": [ "x-intercept of Exponential Functions" ], "current_concepts": [ "Exponential Functions", "x-intercept of Exponential Functions" ] } ## Set $f(x) = 0$ for each function $$ \begin{aligned} 100^{x-5} - 1 &= 0 \ 3^{x-4} + 2 &= 0 \ 7^{x-1} + 1 &= 0 \ -8^{x+1} - 3 &= 0 \end{aligned} $$ ## Solve for real values of $x$ $$ \begin{aligned} 100^{x-5} &= 1 \implies x - 5 = 0 \implies x = 5 \ 3^{x-4} &= -2 \quad (\text{No real solution since } 3^{x-4} > 0) \ 7^{x-1} &= -1 \quad (\text{No real solution since } 7^{x-1} > 0) \ -8^{x+1} &= 3 \implies 8^{x+1} = -3 \quad (\text{No real solution since } 8^{x+1} > 0) \end{aligned} $$ ## Identify the function with a valid x-intercept $$ f(x) = 100^{x-5} - 1 \quad (\text{has } x\text{-intercept at } (5, 0)) $$

(A) $f(x) = 100^{x-5} - 1$

(B) $f(x) = 3^{x-4} + 2$

(C) $f(x) = 7^{x-1} + 1$

(D) $f(x) = -8^{x+1} - 3$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Functions" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Set \(f(x) = 0\) for each function

Solve for real values of \(x\)

Identify the function with a valid x-intercept

Answer: