Question

transformations of the quadratic parent function translations
possible points: 16.67
the quadratic function ( f(x) = x^2 ) is transformed to create the function ( g(x) = f(x + 5.4) - 2.5 ).
choose the correct answer from each drop - down menu to complete the sentence.
the graph of ( f ) is translated 5.4 units (\boldsymbol{
ule{2cm}{0.15mm}}) and 2.5 units (\boldsymbol{
ule{2cm}{0.15mm}}) to create the graph of the function ( g )?

Explanation:

Step1: Recall translation rules for functions

For a function \( y = f(x) \), the transformation \( y = f(x + h) + k \) means: if \( h>0 \), the graph shifts left by \( h \) units; if \( h<0 \), it shifts right. If \( k>0 \), it shifts up by \( k \) units; if \( k<0 \), it shifts down.

Step2: Analyze \( g(x)=f(x + 5.4)-2.5 \)

In \( g(x)=f(x + 5.4)-2.5 \), comparing with \( f(x) \), we have \( h = 5.4 \) (positive, so left shift) and \( k=- 2.5 \) (negative, so down shift). So the graph of \( f \) is translated 5.4 units left and 2.5 units down to create the graph of \( g \).

Answer:

The graph of \( f \) is translated 5.4 units \(\boldsymbol{\text{left}}\) and 2.5 units \(\boldsymbol{\text{down}}\) to create the graph of the function \( g \).