Questions: Evaluate the function at the indicated values. (If ar f(x)=x^2+3 x f(0)= f(3)= f(-3)= f(a)= f(-x)= f(1/a)=

Transcript text: Evaluate the function at the indicated values. (If ar \[ \begin{array}{l} f(x)=x^{2}+3 x \\ f(0)=\square \\ f(3)=\square \\ f(-3)=\square \\ f(a)=\square \\ f(-x)=\square \\ f\left(\frac{1}{a}\right)=\square \end{array} \]

Solution

Solution Steps

Solution Approach

To evaluate the function \( f(x) = x^2 + 3x \) at the indicated values, we will substitute each value into the function and compute the result. Specifically:

For \( f(0) \), substitute \( x = 0 \) into the function.
For \( f(3) \), substitute \( x = 3 \) into the function.
For \( f(-3) \), substitute \( x = -3 \) into the function.
For \( f(a) \), substitute \( x = a \) into the function.
For \( f(-x) \), substitute \( x = -x \) into the function.
For \( f\left(\frac{1}{a}\right) \), substitute \( x = \frac{1}{a} \) into the function.

Step 1: Evaluate \( f(0) \)

Given the function: \[ f(x) = x^2 + 3x \]

We need to evaluate \( f(0) \): \[ f(0) = 0^2 + 3(0) \] \[ f(0) = 0 + 0 \] \[ f(0) = 0 \]

Step 2: Evaluate \( f(3) \)

Next, we evaluate \( f(3) \): \[ f(3) = 3^2 + 3(3) \] \[ f(3) = 9 + 9 \] \[ f(3) = 18 \]

Step 3: Evaluate \( f(-3) \)

Now, we evaluate \( f(-3) \): \[ f(-3) = (-3)^2 + 3(-3) \] \[ f(-3) = 9 - 9 \] \[ f(-3) = 0 \]