question 19 (5 points)
for a given function $f(x)$, the operation $f(3x)$ will
a) shrink the graph horizontally by a factor of $1/3$.
b) shrink the graph vertically by a factor of $1/3$.
c) stretch the graph horizontally by a factor of 3.
d) stretch the graph vertically by a factor of 3.

question 20 (5 points)
multiply the polynomials: $(x - 4)(x^2 + 2x - 5)$
a) $x^3 - 2x^2 - 13x + 20$
b) $x^3 - 2x^2 - 13x - 20$
c) $x^3 + 6x^2 + 3x - 20$
d) $x^3 + 6x^2 + 3x + 20$

Question

question 19 (5 points)
for a given function $f(x)$, the operation $f(3x)$ will
a) shrink the graph horizontally by a factor of $1/3$.
b) shrink the graph vertically by a factor of $1/3$.
c) stretch the graph horizontally by a factor of 3.
d) stretch the graph vertically by a factor of 3.

question 20 (5 points)
multiply the polynomials: $(x - 4)(x^2 + 2x - 5)$
a) $x^3 - 2x^2 - 13x + 20$
b) $x^3 - 2x^2 - 13x - 20$
c) $x^3 + 6x^2 + 3x - 20$
d) $x^3 + 6x^2 + 3x + 20$

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Function Translation" ], "new_concepts": [ "Polynomial Multiplication", "Horizontal Compression" ], "current_concepts": [ "Function Translation", "Polynomial Multiplication", "Horizontal Compression" ] } ## Analyze horizontal scaling in Question 19 $$ \begin{aligned} &g(x) = f(c \cdot x) \text{ with } c = 3 > 1 \ &\text{Horizontal scaling factor: } \frac{1}{c} = \frac{1}{3} \ &\text{Since } 0 < \frac{1}{3} < 1 \text{, the graph shrinks horizontally by a factor of } \frac{1}{3}. \end{aligned} $$ ## Multiply polynomials in Question 20 $$ \begin{aligned} (x - 4)(x^2 + 2x - 5) &= x(x^2 + 2x - 5) - 4(x^2 + 2x - 5) \ &= (x^3 + 2x^2 - 5x) - (4x^2 + 8x - 20) \ &= x^3 + (2 - 4)x^2 + (-5 - 8)x + 20 \ &= x^3 - 2x^2 - 13x + 20 \end{aligned} $$ ## Question 19 A) shrink the graph horizontally by a factor of $1/3$.

B) shrink the graph vertically by a factor of $1/3$.

C) stretch the graph horizontally by a factor of 3.

D) stretch the graph vertically by a factor of 3. ## Question 20 A) $x^3 - 2x^2 - 13x + 20$

B) $x^3 - 2x^2 - 13x - 20$

C) $x^3 + 6x^2 + 3x - 20$

D) $x^3 + 6x^2 + 3x + 20$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Multiplication" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze horizontal scaling in Question 19

Multiply polynomials in Question 20

Answer:

Question 19

Question 20