Question

1. the function value ( f(2)=5 ) means that when ( x = 2 ), the function value is 5. this is equivalent to the ordered pair ( (2,5) ). restate ( f(0)=1 ) and ( f(-3)=-5 ) as ordered pairs.
2. given ( g(x)=2 x^{2}-x ), find

a. ( g(0)=)
b. ( g(-2)=)
c. ( g(3)=)
d. ( g(t)=)
e. ( g(\text{frog})=)
f. ( g(\triangle)=)

1. consider the function defined by ( y = p(x) ) shown to the right. estimate:

a. ( p(-2)=)
b. ( p(3)=)
c. ( p(-4)=)
d. for what value(s) of ( x ) is ( p(x)=0 )?

Explanation:

Step1: Substitute \(x = 0\) into \(g(x)=2x^{2}-x\)

Substitute \(x = 0\) into the function \(g(x)=2x^{2}-x\).

$$
LATEXBLOCK0
$$

Step2: Substitute \(x=-2\) into \(g(x)=2x^{2}-x\)

Substitute \(x = - 2\) into the function \(g(x)=2x^{2}-x\).

$$
LATEXBLOCK1
$$

Step3: Substitute \(x = 3\) into \(g(x)=2x^{2}-x\)

Substitute \(x = 3\) into the function \(g(x)=2x^{2}-x\).

$$
LATEXBLOCK2
$$

Step4: Substitute \(x=t\) into \(g(x)=2x^{2}-x\)

Substitute \(x = t\) into the function \(g(x)=2x^{2}-x\).

$$ g(t)=2t^{2}-t $$

Step5: Substitute \(x = frog\) into \(g(x)=2x^{2}-x\)

Substitute \(x = frog\) into the function \(g(x)=2x^{2}-x\).

$$ g(\text{frog})=2(\text{frog})^{2}-\text{frog} $$

Step6: Substitute \(x=\triangle\) into \(g(x)=2x^{2}-x\)

Substitute \(x=\triangle\) into the function \(g(x)=2x^{2}-x\).

$$ g(\triangle)=2(\triangle)^{2}-\triangle $$

Answer:

a. \(0\)
b. \(10\)
c. \(15\)
d. \(2t^{2}-t\)
e. \(2(\text{frog})^{2}-\text{frog}\)
f. \(2(\triangle)^{2}-\triangle\)