The graph of $y = f(x)$ is shown on the grid below. (a) On the grid above, sketch the graph of $y = f(-x)$ Here is a sketch of the graph of $y = an^2 x$: The graph of $y = an^2 x$ is translated to give the graph of $y = g(x)$. Following the translation the point $Q$, shown on the graph above, moves to point $R$. Point $R$ has coordinates $(90^ ext{o}, -5)$. (b) Find an expression for $g(x)$ in terms of $x$.

Photo AI

The graph of $y = f(x)$ is shown on the grid below - Edexcel - GCSE Maths - Question 22 - 2022 - Paper 2

Question 22

The graph of $y = f(x)$ is shown on the grid below. (a) On the grid above, sketch the graph of $y = f(-x)$ Here is a sketch of the graph of $y = an^2 x$: The gra... show full transcript

Worked Solution & Example Answer:The graph of $y = f(x)$ is shown on the grid below - Edexcel - GCSE Maths - Question 22 - 2022 - Paper 2

Step 1

a) On the grid above, sketch the graph of $y = f(-x)$

96%

114 rated

Answer

To sketch the graph of $y = f(-x)$ , reflect the original graph $y = f(x)$ across the $y$ -axis. Keep the shape and points of the original graph, but invert the $x$ -coordinates. This will include the downward parts of the graph becoming upward, as well as all features being mirrored to the opposite side of the $y$ -axis.

Step 2

b) Find an expression for $g(x)$ in terms of $x$.

99%

104 rated

Answer

The transformation of point $Q$ with coordinates $(x_0, y_0)$ to point $R$ with coordinates $(90^ ext{o}, -5)$ indicates that $g(x)$ is reached by first translating $x$ by $90^ ext{o}$ . Hence, if the original function is $y = an^2 heta$ , we can express it as:

g(x) = an^2(270 - x), ext{ where } x ext{ is a real number and } x eq 0$.

Join the GCSE students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;