use a graphing utility to graph the function. then use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one).

(f(x) = |x - 4|)

choose the correct graph of (f(x) = |x - 4|). each tick mark is one unit.

a.
b.
c.
d.

Question

use a graphing utility to graph the function. then use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one).

(f(x) = |x - 4|)

choose the correct graph of (f(x) = |x - 4|). each tick mark is one unit.

a.
b.
c.
d.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "One-to-One Functions", "Horizontal Line Test" ], "new_concepts": [ "Absolute Value Functions" ], "current_concepts": [ "One-to-One Functions", "Horizontal Line Test", "Absolute Value Functions" ] } ## Identify the function and its vertex Using the *One-to-One Functions* knowledge point $$ \begin{aligned} &f(x) = |x - 4|\ &\text{Vertex: } (4, 0)\ &\text{y-intercept: } (0, 4) \end{aligned} $$ ## Match the function to the correct graph Using the *One-to-One Functions* knowledge point $$ \begin{aligned} &\text{Graph A vertex: } (-4, 0)\ &\text{Graph B vertex: } (4, 0)\ &\text{Graph C vertex: } (-4, 0) \text{ (inverted)}\ &\text{Graph D vertex: } (4, 0) \text{ (inverted)}\ &\text{Correct Graph: } \text{B} \end{aligned} $$ ## Determine if the function is one-to-one Using the *Horizontal Line Test* knowledge point $$ \begin{aligned} &\text{Horizontal line } y = 2 \text{ intersects } f(x) \text{ at } x = 2 \text{ and } x = 6.\ &\text{Since a horizontal line intersects the graph more than once, the function is not one-to-one.}\ &\text{Therefore, the function does not have an inverse that is a function.} \end{aligned} $$

(A) Graph A; the function has an inverse that is a function

(B) Graph B; the function does not have an inverse that is a function

(C) Graph C; the function has an inverse that is a function

(D) Graph D; the function does not have an inverse that is a function

{ "elements": [ { "type": "functiongraph", "params": [ { "js": "Math.abs(x - 4)", "latex": "|x - 4|" }, -10, 10 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3, "name": "f(x) = |x - 4|", "withLabel": true } }, { "type": "point", "params": [ [4, 0] ], "properties": { "name": "Vertex (4,0)", "size": 4, "color": "#F2557F", "withLabel": true } }, { "type": "line", "params": [ [-10, 2], [10, 2] ], "properties": { "strokeColor": "#5583F2", "strokeWidth": 1.5, "strokeDash": 2, "name": "y = 2", "withLabel": true } }, { "type": "point", "params": [ [2, 2] ], "properties": { "name": "(2,2)", "size": 3, "color": "#5583F2", "withLabel": true } }, { "type": "point", "params": [ [6, 2] ], "properties": { "name": "(6,2)", "size": 3, "color": "#5583F2", "withLabel": true } } ], "timestamps": [0.5, 1.0, 1.5] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "One-to-One Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the function and its vertex

Match the function to the correct graph

Determine if the function is one-to-one

Answer: