Question
The graph of f(x)=x3
is transformed by multiplying the function by a factor of a=14
. Identify the new coordinate for x=4
after f(x)
is vertically compressed.(1 point)
The new coordinates are (
,
).
is transformed by multiplying the function by a factor of a=14
. Identify the new coordinate for x=4
after f(x)
is vertically compressed.(1 point)
The new coordinates are (
,
).
Answers
GPT-4o mini
To transform the function \( f(x) = x^3 \) by multiplying it by a factor of \( a = 14 \), we can express the transformed function as:
\[
g(x) = 14 \cdot f(x) = 14 \cdot x^3
\]
Next, we need to find the new coordinate for \( x = 4 \):
1. First, calculate \( f(4) \):
\[
f(4) = 4^3 = 64
\]
2. Now, calculate \( g(4) \):
\[
g(4) = 14 \cdot f(4) = 14 \cdot 64 = 896
\]
Thus, the new coordinates after the transformation for \( x = 4 \) are:
\[
(4, 896)
\]
So, the new coordinates are \( (4, 896) \).
\[
g(x) = 14 \cdot f(x) = 14 \cdot x^3
\]
Next, we need to find the new coordinate for \( x = 4 \):
1. First, calculate \( f(4) \):
\[
f(4) = 4^3 = 64
\]
2. Now, calculate \( g(4) \):
\[
g(4) = 14 \cdot f(4) = 14 \cdot 64 = 896
\]
Thus, the new coordinates after the transformation for \( x = 4 \) are:
\[
(4, 896)
\]
So, the new coordinates are \( (4, 896) \).