which is the graph of $f(x) = 0.5(4)^x$?

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Exponential Functions", "y-intercept", "Exponential Growth" ], "new_concepts": [], "current_concepts": [ "Exponential Functions", "y-intercept", "Exponential Growth" ] } ## Evaluate the function at key points $$ \begin{aligned} f(0) &= 0.5(4)^0 = 0.5(1) = 0.5 \ f(1) &= 0.5(4)^1 = 2 \ f(2) &= 0.5(4)^2 = 0.5(16) = 8 \ f(3) &= 0.5(4)^3 = 0.5(64) = 32 \end{aligned} $$ ## Verify points on the given graph $$ \begin{aligned} (0, 0.5) &\implies \text{Passes near origin just above } y = 0 \ (2, 8) &\implies \text{Passes through } (2, 8) \text{ (halfway to 16)} \ (3, 32) &\implies \text{Passes exactly through } (3, 32) \end{aligned} $$ ## Match with the correct option The shown graph correctly plots the points $(0, 0.5)$, $(2, 8)$, and $(3, 32)$.

(A) The graph passing through (0, 0.5), (2, 8), and (3, 32)

(B) The graph passing through (0, 0.5), (1, 4), and (2, 16)

{ "elements": [ { "type": "functiongraph", "params": [ { "js": "0.5 * Math.pow(4, x)", "latex": "0.5 \cdot 4^x" }, -4, 4 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3 } }, { "type": "point", "params": [[0, 0.5]], "properties": { "name": "(0, 0.5)", "size": 4, "color": "#5583F2", "withLabel": true } }, { "type": "point", "params": [[2, 8]], "properties": { "name": "(2, 8)", "size": 4, "color": "#5583F2", "withLabel": true } }, { "type": "point", "params": [[3, 32]], "properties": { "name": "(3, 32)", "size": 4, "color": "#5583F2", "withLabel": true } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Functions" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Evaluate the function at key points

Verify points on the given graph

Match with the correct option

Answer: