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
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 $\square$
Solution
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, where m is the slope (rate of change) and 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 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, where m is the slope and b is the y-intercept.
Step 2: Determine the Form of the Function
Given the form f(x)=mx+b, we can substitute the values m=2 and b=3 into the equation. Thus, the function becomes:
f(x)=2x+3
Step 3: Calculate the Value of the Function
To find the value of the function at x=5, substitute x=5 into the equation:
f(5)=2(5)+3=10+3=13
Final Answer
(a) The function f is a linear function and f(x)=2x+3.