The graph of $y = f(x)$ is shown on the grid. (a) On the grid, draw the graph with equation $y = f(x + 1) - 3$. Point $A(-2, 1)$ lies on the graph of $y = f(x)$. When the graph of $y = f(x)$ is transformed to the graph with equation $y = f(-x)$, point $A$ is mapped to point $B$. (b) Write down the coordinates of point $B$.

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The graph of $y = f(x)$ is shown on the grid - Edexcel - GCSE Maths - Question 21 - 2019 - Paper 1

Question 21

The graph of $y = f(x)$ is shown on the grid. (a) On the grid, draw the graph with equation $y = f(x + 1) - 3$. Point $A(-2, 1)$ lies on the graph of $y = f(x)$. W... show full transcript

Worked Solution & Example Answer:The graph of $y = f(x)$ is shown on the grid - Edexcel - GCSE Maths - Question 21 - 2019 - Paper 1

Step 1

Draw the graph with equation $y = f(x + 1) - 3$

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Answer

To draw the graph of $y = f(x + 1) - 3$ , we first shift the original graph of $y = f(x)$ to the left by 1 unit and then downward by 3 units. This means every point $(x, f(x))$ on the original graph is transformed to the new point $(x - 1, f(x) - 3)$ , effectively translating the graph accordingly.

Step 2

Write down the coordinates of point B

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Answer

To find point $B$ , we need to apply the transformation given by the equation $y = f(-x)$ to point $A(-2, 1)$ .

The transformation $x ightarrow -x$ reflects point $A$ across the $y$ -axis. Thus, the $x$ -coordinate becomes $2$ .
The $y$ -coordinate remains unchanged, so point $B$ will have coordinates $(2, 1)$ .

Therefore, the coordinates of point $B$ are $(2, 1)$ .

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