Questions: Let f be a function with constant rate of change. (a) Then f is a function and f is of the form f(x)= x+ . (b) The graph of f is

Let f be a function with constant rate of change. (a) Then f is a function and f is of the form f(x)= x+ . (b) The graph of f is
Transcript text: Let $f$ be a function with constant rate of change. (a) Then $f$ is a $\square$ function and $f$ is of the form $f(x)=$ $\square$ $x+$ $\square$ . (b) The graph of $f$ is $\square$
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Solution

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Solution Steps

To solve this problem, we need to identify the type of function that has a constant rate of change. This type of function is a linear function. A linear function can be expressed in the form f(x)=mx+b f(x) = mx + b , where m m is the slope (rate of change) and b b is the y-intercept. The graph of a linear function is a straight line.

Step 1: Identify the Type of Function

The function f f has a constant rate of change, which indicates that it is a linear function. A linear function can be expressed in the form f(x)=mx+b f(x) = mx + b , where m m is the slope and b b is the y-intercept.

Step 2: Determine the Form of the Function

Given the form f(x)=mx+b f(x) = mx + b , we can substitute the values m=2 m = 2 and b=3 b = 3 into the equation. Thus, the function becomes: f(x)=2x+3 f(x) = 2x + 3

Step 3: Calculate the Value of the Function

To find the value of the function at x=5 x = 5 , substitute x=5 x = 5 into the equation: f(5)=2(5)+3=10+3=13 f(5) = 2(5) + 3 = 10 + 3 = 13

Final Answer

(a) The function f f is a linear\boxed{\text{linear}} function and f(x)=2x+3 f(x) = \boxed{2x + 3} .

(b) The graph of f f is a straight line\boxed{\text{straight line}}.

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