Question

unit 1.2 functions and graphs day 1 homework date:

1. given that ( g(x) = x^3 ), find each of the following:

a. ( g(3) )
b. ( g(-2) )
c. ( g(-x) )
d. ( g(4z) )

1. given that ( f(x) = -2x^2 + x - 1 ), find each of the following:

a. ( f(0) )
b. ( f(2) )
c. ( f(-2) )
d. ( f(-q) )
e. ( f(1 - y) )
f. ( f(3w) )

Explanation:

Step1: Evaluate \(g(3)\)

Substitute \(x=3\) into \(g(x)=x^3\):
\(g(3)=3^3=27\)

Step2: Evaluate \(g(-2)\)

Substitute \(x=-2\) into \(g(x)=x^3\):
\(g(-2)=(-2)^3=-8\)

Step3: Evaluate \(g(-x)\)

Substitute \(x=-x\) into \(g(x)=x^3\):
\(g(-x)=(-x)^3=-x^3\)

Step4: Evaluate \(g(4z)\)

Substitute \(x=4z\) into \(g(x)=x^3\):
\(g(4z)=(4z)^3=64z^3\)

Step5: Evaluate \(f(0)\)

Substitute \(x=0\) into \(f(x)=-2x^2+x-1\):
\(f(0)=-2(0)^2+0-1=-1\)

Step6: Evaluate \(f(2)\)

Substitute \(x=2\) into \(f(x)=-2x^2+x-1\):
\(f(2)=-2(2)^2+2-1=-8+2-1=-7\)

Step7: Evaluate \(f(-2)\)

Substitute \(x=-2\) into \(f(x)=-2x^2+x-1\):
\(f(-2)=-2(-2)^2+(-2)-1=-8-2-1=-11\)

Step8: Evaluate \(f(-q)\)

Substitute \(x=-q\) into \(f(x)=-2x^2+x-1\):
\(f(-q)=-2(-q)^2+(-q)-1=-2q^2-q-1\)

Step9: Evaluate \(f(1-y)\)

Substitute \(x=1-y\) into \(f(x)=-2x^2+x-1\):
\[

$$\begin{align*} f(1-y)&=-2(1-y)^2+(1-y)-1\\ &=-2(1-2y+y^2)+1-y-1\\ &=-2+4y-2y^2-y\\ &=-2y^2+3y-2 \end{align*}$$

\]

Step10: Evaluate \(f(3w)\)

Substitute \(x=3w\) into \(f(x)=-2x^2+x-1\):
\[

$$\begin{align*} f(3w)&=-2(3w)^2+3w-1\\ &=-2(9w^2)+3w-1\\ &=-18w^2+3w-1 \end{align*}$$

\]

Answer:

1.
a. \(27\)
b. \(-8\)
c. \(-x^3\)
d. \(64z^3\)
2.
a. \(-1\)
b. \(-7\)
c. \(-11\)
d. \(-2q^2-q-1\)
e. \(-2y^2+3y-2\)
f. \(-18w^2+3w-1\)