Question

Evaluate the function f when we have at the indicated values.f(x)=x^2-3xf(5)=Answersolve f(x)=4 Type your answers from smallest to largest.If f(x)=4 then x=Answer and AnswerThis graph Answer represent a function.This graph Answer represent a one-to-one function.

Answer 1

Given the function:

`f(x)=x^2-3x`

Let's solve for f(5).

To solve the function f when we have the indicated value f(5), substitute 5 for x in the function and solve.

Thus, we have:

`\begin{gathered} f(5)=5^2-3(5) \\ \\ f(5)=25-15 \\ \\ f(5)=10 \end{gathered}`

Let's solve for f(x) = 4.

To solve when f(x) = 4, substitute 4 for f(x) amd solve for the values of x.

Thus, we have:

`\begin{gathered} 4=x^2-3x \\ \\ x^2-3x=4 \\ \\ \text{Subtract 4 from both sides:} \\ x^2-3x-4=4-4 \\ \\ x^2-3x-4=0 \end{gathered}`

Factorize the left side using the AC method:

Find a pair of numbers whose product is 4 and sum is -3.

We have:

-4 and 1

`(x-4)(x+1)=0`

Set each factor to zero and solve for x:

`\begin{gathered} x-4=0 \\ \text{Add 4 to both sides:} \\ x-4+4=0+4 \\ x=4 \\ \\ x+1=0 \\ \text{Subtract 1 from both sides:} \\ x+1-1=0-1 \\ \\ x=-1 \end{gathered}`

Therefore, if f(x) = 4, then x = 4 and -1.

The grap represents a function because it passes the vertical line test.

The graph does not represent a one-to-one function.

ANSWER:

• f(5) = 10

,

• If f(x) = 4 then x = 4 and -1

,

• The graph represents a function.

,

• The graph does not represent a one-to-one function.