Question

homework assignment 1.1: functions and function notation
score: 6/15 answered: 6/15
question 7
given the function $f(x) = 4x^2 - 8x + 3$. calculate the following values:
$f(-2) = $
$f(-1) = $
$f(0) = $
$f(1) = $
$f(2) = $
question help: video written example

Explanation:

Step1: Calculate \( f(-2) \)

Substitute \( x = -2 \) into \( f(x) = 4x^2 - 8x + 3 \).
\[

$$\begin{align*} f(-2)&= 4(-2)^2 - 8(-2) + 3\\ &= 4(4) + 16 + 3\\ &= 16 + 16 + 3\\ &= 35 \end{align*}$$

\]

Step2: Calculate \( f(-1) \)

Substitute \( x = -1 \) into \( f(x) = 4x^2 - 8x + 3 \).
\[

$$\begin{align*} f(-1)&= 4(-1)^2 - 8(-1) + 3\\ &= 4(1) + 8 + 3\\ &= 4 + 8 + 3\\ &= 15 \end{align*}$$

\]

Step3: Calculate \( f(0) \)

Substitute \( x = 0 \) into \( f(x) = 4x^2 - 8x + 3 \).
\[

$$\begin{align*} f(0)&= 4(0)^2 - 8(0) + 3\\ &= 0 - 0 + 3\\ &= 3 \end{align*}$$

\]

Step4: Calculate \( f(1) \)

Substitute \( x = 1 \) into \( f(x) = 4x^2 - 8x + 3 \).
\[

$$\begin{align*} f(1)&= 4(1)^2 - 8(1) + 3\\ &= 4 - 8 + 3\\ &= -1 \end{align*}$$

\]

Step5: Calculate \( f(2) \)

Substitute \( x = 2 \) into \( f(x) = 4x^2 - 8x + 3 \).
\[

$$\begin{align*} f(2)&= 4(2)^2 - 8(2) + 3\\ &= 4(4) - 16 + 3\\ &= 16 - 16 + 3\\ &= 3 \end{align*}$$

\]

Answer:

\( f(-2) = 35 \)
\( f(-1) = 15 \)
\( f(0) = 3 \)
\( f(1) = -1 \)
\( f(2) = 3 \)