Question
Consider the exponential function, f(x)=4x
Reflect f(x)
across the x
axis and then shift the function up 3
units.
Write the new expression for f(x)
after both transformations.
(2 points)
Reflect f(x)
across the x
axis and then shift the function up 3
units.
Write the new expression for f(x)
after both transformations.
(2 points)
Answers
GPT-4o mini
To reflect the function \( f(x) = 4^x \) across the x-axis, we multiply the function by -1. This gives us:
\[
f(x) = -4^x
\]
Next, we shift the function up 3 units. To do this, we add 3 to the entire function:
\[
f(x) = -4^x + 3
\]
Therefore, the new expression for \( f(x) \) after both transformations is:
\[
f(x) = -4^x + 3
\]
\[
f(x) = -4^x
\]
Next, we shift the function up 3 units. To do this, we add 3 to the entire function:
\[
f(x) = -4^x + 3
\]
Therefore, the new expression for \( f(x) \) after both transformations is:
\[
f(x) = -4^x + 3
\]