Transformations of Graphs
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Transformations of Graphs — Free MYP4 Mathematics (Standard) Practice Questions

1QuestionStretching and Compressing GraphsConcept Practice
4 marks~6 minCriterion A
A solar panel manufacturer models the power output (in watts) of a panel using the function f(x)=x2f(x) = x^2, where xx is the number of hours after sunrise. A premium panel has greater output, modelled by g(x)=a f(x)g(x) = a\,f(x).

The premium panel produces 48 watts exactly 4 hours after sunrise.
a
Deduce the value of aa. [2]
b
Explain what the value of aa means for the power output of the premium panel compared to the standard panel at every hour of the day. [2]
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Solutions

2QuestionCombining Multiple TransformationsAssessment Practice
4 marks~6 minCriterion C
A drone follows a flight path modelled by f(x)=x2f(x) = x^2, where xx is horizontal distance (metres) and f(x)f(x) is height (metres). An adjusted path is modelled by g(x)=(x+3)2−5g(x) = (x+3)^2 - 5.

A safety regulation states that the drone must remain at or above −4-4 metres relative to the launch reference height.
a
State the coordinates of the vertex of g(x)g(x). [1]
b
Explain how the graph of g(x)g(x) is obtained from the graph of f(x)f(x) through translations. [2]
c
Evaluate g(−2)g(-2) and justify whether the drone satisfies the safety regulation at x=−2x = -2. [1]
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Solutions

3QuestionCombining Multiple TransformationsAssessment Practice
4 marks~6 minCriterion D
A telecommunications company models the height (in km) of a satellite dish's signal beam using

y=−2(x−3)2+5y = -2(x-3)^2 + 5

where xx is the horizontal distance in kilometres from the dish. The parent function is y=x2y = x^2.
a
Describe the sequence of transformations applied to y=x2y = x^2 to obtain y=−2(x−3)2+5y = -2(x-3)^2 + 5. [2]
b
Explain one mathematical advantage of using this form of the equation to identify the optimal signal coverage position. [1]
c
The company claims the model is reliable for all distances x≥0x \geq 0. Advise the company whether this claim should be accepted, supporting your answer with both a mathematical and a physical reason. [1]
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Solutions

4QuestionTranslating Graphs Vertically and HorizontallyAssessment Practice
6 marks~9 minCriterion B
A drone delivery company models the height of a package above ground during a test drop using the parent function f(x)=x2f(x) = x^2, where xx is horizontal distance (metres) from the drop point. Engineers test three adjusted flight paths: g(x)=x2+1g(x) = x^2 + 1, h(x)=x2−3h(x) = x^2 - 3, and j(x)=x2+5j(x) = x^2 + 5.
a
Calculate the yy-values for f(x)f(x), g(x)g(x), h(x)h(x), and j(x)j(x) at x=−2, −1, 0, 1, 2x = -2,\ -1,\ 0,\ 1,\ 2. Complete the table below. [2]

xx: −2-2, −1-1, 00, 11, 22

f(x)f(x): \_\_\_, \_\_\_, \_\_\_, \_\_\_, \_\_\_

g(x)g(x): \_\_\_, \_\_\_, \_\_\_, \_\_\_, \_\_\_

h(x)h(x): \_\_\_, \_\_\_, \_\_\_, \_\_\_, \_\_\_

j(x)j(x): \_\_\_, \_\_\_, \_\_\_, \_\_\_, \_\_\_
b
Analyse the relationship between the yy-values of g(x)g(x), h(x)h(x), and j(x)j(x) and those of f(x)f(x). Deduce a general rule describing how adding a constant cc to x2x^2 transforms the graph of y=x2y = x^2. [2]
c
A safe landing requires the package height at x=0x = 0 to remain above −5-5 metres. A new flight path is modelled by k(x)=x2−7k(x) = x^2 - 7. Using your rule from part (b), advise the engineers whether this flight path should be approved, justifying your answer with reference to the safety requirement. [2]

Solutions

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