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 Function Graphs", "Graph Intercepts" ], "new_concepts": [], "current_concepts": [ "Exponential Function Graphs", "Graph Intercepts" ] } ## Define the condition for an x-intercept $$ f(x) = 0 $$ ## Test each given function for a real solution $$ \begin{aligned} &100^{x-5} - 1 = 0 \implies 100^{x-5} = 1 \implies x-5 = 0 \implies x = 5 \ &3^{x-4} + 2 = 0 \implies 3^{x-4} = -2 \quad (\text{No real solution}) \ &7^{x-1} + 1 = 0 \implies 7^{x-1} = -1 \quad (\text{No real solution}) \ &-8^{x+1} - 3 = 0 \implies -8^{x+1} = 3 \implies 8^{x+1} = -3 \quad (\text{No real solution}) \end{aligned} $$ ## Identify the correct option $$ f(x) = 100^{x-5} - 1 \text{ has a real } x\text{-intercept at } x = 5. $$

(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 Function Graphs" ] }

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QUESTION IMAGE

Question

Explanation:

Define the condition for an x-intercept

Test each given function for a real solution

Identify the correct option

Answer: