We will see that g(x) is a reflection across the y-axis of f(x), then:
By looking at the graph, we can see that g(x) is a reflection across the y-axis of f(x).
So we can write:
g(x) = f(-x)
Here we know that:
Then, replacing f(x) on the formula for g(x), we get:
That is the function g(x) shown in the figure.
If you want to learn more about transformations:
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Given:
The equation goes through the coordinates (6,5) and (-2,-5).
To find:
The values of A and B.
Solution:
We have,
It goes through the coordinates (6,5) and (-2,-5). It means these points will satisfy the equation.
...(i)
...(ii)
Adding (i) and (ii), we get
Divide both sides by 4.
Put A=5 in (i), we get
Divide both sides by 5.
Therefore, the values of A and B are 5 and -4 respectively.