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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 $y = f(x + 1) - 3$.
Answer
To graph the equation , 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 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.
Answer
To determine the coordinates of point B, we first establish the transformation from point A(-2, 1) to point B through the transformation .
The x-coordinate of point B will be the negative of the x-coordinate of point A: .
The y-coordinate remains the same as point A: .
Thus, the coordinates of point B are: