Answer:
Reflection across y axis
Translate up by 3 units
Step-by-step explanation:
Given
[tex]f(x) = x + 1[/tex]
[tex]g(x) = -x + 4[/tex]
Required
Describe the transformation from f(x) to g(x)
First, take a reflection of f(x) across the y axis.
So f(x) becomes f(-x)
[tex]f(x) = x + 1[/tex] when reflected
[tex]f(-x) = -x +1[/tex]
Next, translate f(-x) up by 3 units to give g(x)
[tex]g(x) = f(-x) + k[/tex]
Where
[tex]k = 3[/tex]
[tex]f(-x) = -x +1[/tex]
[tex]g(x) = -x + 1 + 3[/tex]
[tex]g(x) = -x + 4[/tex]
Hence, the transformation from f(x) to g(x) includes:
Reflection across y axis
Translate up by 3 units
