Exam-Style Questions.

Problems adapted from questions set for previous Mathematics exams.

1.

GCSE Higher

The graph of the curve A with equation $$y=f(x)$$ is transformed to give the graph of the curve B with equation $$y=5-f(x)$$.

The point on A with coordinates (3, 9) is mapped to the point W on B.

Find the coordinates of W.

2.

GCSE Higher

The graph of the following equation is drawn and then reflected in the x-axis

$$y = 2x^2 - 3x + 2$$

(a) What is the equation of the reflected curve?

The original curve is reflected in the y-axis.

(b) What is the equation of this second reflected curve?

3.

IB Standard

$$f$$ and $$g$$ are two functions such that $$g(x)=3f(x+2)+7$$.

The graph of $$f$$ is mapped to the graph of $$g$$ under the following transformations:

A vertical stretch by a factor of $$a$$ , followed by a translation $$\begin{pmatrix}b \\c \\ \end{pmatrix}$$

Find the values of

(a) $$a$$;

(b) $$b$$;

(c) $$c$$.

(d) Consider two other functions $$h$$ and $$j$$. Let $$h(x)=-j(2x)$$. The point A(8, 7) on the graph of $$j$$ is mapped to the point B on the graph of $$h$$. Find the coordinates of B.

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