Questions: QUESTION 14 - 1 POINT Consider the table of values below. x 0 1 2 3 f(x) 1 18 35 52 Find the linear function f(x) that corresponds to the table of values. Provide your answer below: f(x)=

QUESTION 14 - 1 POINT Consider the table of values below. x 0 1 2 3 f(x) 1 18 35 52 Find the linear function f(x) that corresponds to the table of values. Provide your answer below: f(x)=
Transcript text: QUESTION 14 - 1 POINT Consider the table of values below. \begin{tabular}{c|cccc} $x$ & 0 & 1 & 2 & 3 \\ \hline$f(x)$ & 1 & 18 & 35 & 52 \end{tabular} Find the linear function $f(x)$ that corresponds to the table of values. Provide your answer below: \[ f(x)= \] $\square$
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Solution

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Solution Steps

To find the linear function \( f(x) \) that corresponds to the given table of values, we need to determine the slope and the y-intercept of the line. The slope \( m \) can be calculated using the formula \( m = \frac{f(x_2) - f(x_1)}{x_2 - x_1} \). Once the slope is determined, we can use one of the points to solve for the y-intercept \( b \) using the equation \( f(x) = mx + b \).

Step 1: Calculate the Slope

To find the slope \( m \) of the linear function, we use the formula: \[ m = \frac{f(x_2) - f(x_1)}{x_2 - x_1} \] Using the points \( (0, 1) \) and \( (1, 18) \): \[ m = \frac{18 - 1}{1 - 0} = 17.0 \]

Step 2: Calculate the Y-Intercept

Next, we calculate the y-intercept \( b \) using the point-slope form of the linear equation: \[ f(x) = mx + b \] Substituting \( m = 17.0 \) and using the point \( (0, 1) \): \[ 1 = 17.0 \cdot 0 + b \implies b = 1.0 \]

Step 3: Write the Linear Function

Now that we have both \( m \) and \( b \), we can express the linear function: \[ f(x) = 17.0x + 1.0 \]

Final Answer

The linear function corresponding to the table of values is \[ \boxed{f(x) = 17.0x + 1.0} \]

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