consider the graph of the function $f(x) = 10^x$

what is the y-intercept of function $g$ if $g(x) = -4f(x) + 12$?

(0, 8)
(0, 1)
(0, 12)
(0, -4)

Question

consider the graph of the function $f(x) = 10^x$

what is the y-intercept of function $g$ if $g(x) = -4f(x) + 12$?

(0, 8)
(0, 1)
(0, 12)
(0, -4)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Graph Intercepts", "Function Transformations" ], "new_concepts": [], "current_concepts": [ "Graph Intercepts", "Function Transformations", "Exponential Functions" ] } ## Find the y-intercept of the base function $$ \begin{aligned} f(x) &= 10^x \ f(0) &= 10^0 = 1 \end{aligned} $$ ## Evaluate the transformed function at x = 0 $$ \begin{aligned} g(x) &= -4f(x) + 12 \ g(0) &= -4f(0) + 12 \ g(0) &= -4(1) + 12 = 8 \end{aligned} $$ ## State the y-intercept coordinate $$ (0, 8) $$

(A) (0,8)

(B) (0,1)

(C) (0,12)

(D) (0,-4)

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Function Transformations" ] }

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QUESTION IMAGE

Question

Explanation:

Find the y-intercept of the base function

Evaluate the transformed function at x = 0

State the y-intercept coordinate

Answer: