Question

202620:23481 college algebra (math-1314-752)
homework 16: section 3.4
determine $f(-4) = \square$
determine $g(-4) = \square$
determine $(f + g)(-4) = \square$
determine $f(-3) = \square$
determine $g(-3) = \square$
determine $(f - g)(-3) = \square$
determine $f(1) = \square$
determine $g(1) = \square$
determine $(g - f)(1) = \square$
determine $f(2) = \square$
determine $g(2) = \square$
determine $(fg)(2) = \square$

Explanation:

For \( f(-4) \):

Step1: Find \( f(-4) \) from graph

Look at the graph of \( f(x) \), at \( x = -4 \), the y - value (function value) is the y - coordinate of the point on \( f(x) \)'s graph. From the left graph (for \( f(x) \)), at \( x=-4 \), the point is at \( y = - 2 \). So \( f(-4)=-2 \).

For \( g(-4) \):

Step1: Find \( g(-4) \) from graph

Look at the graph of \( g(x) \), at \( x = -4 \), the y - value (function value) is the y - coordinate of the point on \( g(x) \)'s graph. From the right graph (for \( g(x) \)), at \( x = - 4 \), the point is at \( y=1 \). So \( g(-4) = 1 \).

For \( (f + g)(-4) \):

Step1: Recall the formula for sum of functions

The formula for \( (f + g)(x)=f(x)+g(x) \). So \( (f + g)(-4)=f(-4)+g(-4) \).

Step2: Substitute the values

We know \( f(-4)=-2 \) and \( g(-4) = 1 \). Then \( (f + g)(-4)=-2 + 1=-1 \).

For \( f(-3) \):

Answer:

s:
\( f(-4)=\boldsymbol{-2} \)

\( g(-4)=\boldsymbol{1} \)

\( (f + g)(-4)=\boldsymbol{-1} \)

\( f(-3)=\boldsymbol{-2} \)

\( g(-3)=\boldsymbol{0} \)

\( (f - g)(-3)=\boldsymbol{-2} \)

\( f(1)=\boldsymbol{1} \)

\( g(1)=\boldsymbol{1} \)

\( (g - f)(1)=\boldsymbol{0} \)

\( f(2)=\boldsymbol{0} \)

\( g(2)=\boldsymbol{3} \)

\( (fg)(2)=\boldsymbol{0} \)