question 7 (5 points)
for a given function $f(x) = x^2 - x + 1$, the operation $-f(x) = -(x^2 - x + 1)$ will result in a
a) reflection across the x-axis.
b) horizontal shrink.
c) vertical shrink.
d) reflection across the y-axis.

question 8 (5 points)
which of these is a factor of $x^3 - 3x^2$?
a) $x + 2$
b) $x + 3$
c) $x - 2$
d) $x - 3$

Question

question 7 (5 points)
for a given function $f(x) = x^2 - x + 1$, the operation $-f(x) = -(x^2 - x + 1)$ will result in a
a) reflection across the x-axis.
b) horizontal shrink.
c) vertical shrink.
d) reflection across the y-axis.

question 8 (5 points)
which of these is a factor of $x^3 - 3x^2$?
a) $x + 2$
b) $x + 3$
c) $x - 2$
d) $x - 3$

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Function Transformations", "Greatest Common Factor Factoring" ], "new_concepts": [], "current_concepts": [ "Function Transformations", "Greatest Common Factor Factoring" ] } ## Analyze Question 7 Using the *Function Transformations* knowledge point $$ \begin{aligned} &g(x) = -f(x)\ &\text{Since } g(x) = -f(x) \text{ negates the output values, it reflects the graph vertically across the } x\text{-axis.} \end{aligned} $$ ## Analyze Question 8 Using the *Greatest Common Factor Factoring* knowledge point $$ \begin{aligned} &x^3 - 3x^2 = x^2(x - 3)\ &\text{The factors are } x^2 \text{ and } (x - 3). \end{aligned} $$ ## Question 7 (A) reflection across the x-axis.

(B) horizontal shrink.

(C) vertical shrink.

(D) reflection across the y-axis. ## Question 8 (A) x + 2

(B) x + 3

(C) x - 2

(D) x - 3

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

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