which equation represents the function $f(x) = (1.6)^x$ after it has been translated 5 units up and 9 units to the right?

$g(x) = (1.6)^{x + 5} - 9$
$g(x) = (1.6)^{x + 5} + 9$
$g(x) = (1.6)^{x - 9} + 5$
$g(x) = (1.6)^{x + 9} + 5$

Question

which equation represents the function $f(x) = (1.6)^x$ after it has been translated 5 units up and 9 units to the right?

$g(x) = (1.6)^{x + 5} - 9$
$g(x) = (1.6)^{x + 5} + 9$
$g(x) = (1.6)^{x - 9} + 5$
$g(x) = (1.6)^{x + 9} + 5$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Function Transformations", "Exponential Functions" ], "new_concepts": [], "current_concepts": [ "Function Transformations", "Exponential Functions" ] } ## Apply horizontal translation Using the *Function Transformations* and *Exponential Functions* knowledge points $$ \begin{aligned} &f(x) = (1.6)^x\ &h(x) = f(x - 9) = (1.6)^{x - 9} \end{aligned} $$ ## Apply vertical translation Using the *Function Transformations* knowledge point $$ \begin{aligned} &g(x) = h(x) + 5\ &g(x) = (1.6)^{x - 9} + 5 \end{aligned} $$

(A) $g(x) = (1.6)^{x + 5} - 9$

(B) $g(x) = (1.6)^{x + 5} + 9$

(C) $g(x) = (1.6)^{x - 9} + 5$

(D) $g(x) = (1.6)^{x + 9} + 5$

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

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QUESTION IMAGE

Question

Explanation:

Apply horizontal translation

Apply vertical translation

Answer: