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

On the grid, draw the graph with equation $y = f(x + 1) - 3$.

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Answer

To graph the equation $y = f(x + 1) - 3$ , we need to recognize that this involves a horizontal translation left by 1 unit and a vertical translation down by 3 units.

Start by identifying the original graph of $y = f(x)$ given in the problem.
Shift all points of the graph 1 unit to the left. For instance, if point A is at (-2, 1), it will move to (-3, 1).
Then, move every point down by 3 units. The new position of point A will be at (-3, -2).

Repeat this operation for all points, ensuring that the shape and features of the graph remain consistent.

Step 2

Write down the coordinates of point B.

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Answer

To determine the coordinates of point B, we first establish the transformation from point A(-2, 1) to point B through the transformation $y = f(-x)$ .

The x-coordinate of point B will be the negative of the x-coordinate of point A: $B_x = -(-2) = 2$ .

The y-coordinate remains the same as point A: $B_y = A_y = 1$ .

Thus, the coordinates of point B are:

$B(2, 1)$

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

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

On the grid, draw the graph with equation $y = f(x + 1) - 3$.

Write down the coordinates of point B.

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