Get the complete, step-by-step math solution for: "Let {R} be the set of real numbers. Define the real function f: {R} → {R} { by } f(x)=x+10 and sketch the graph of this function.". Powered by SolveForX AI math tutor.
Step 1: Understand the Function
The given function is a linear function of the form f(x)=mx+c, where m is the slope and c is the y -intercept. In this case, the slope m=1 and the y -intercept c=10.
Step 2: Find Key Points
To sketch a linear function, we need at least two points. Let's choose a few simple x values and calculate their corresponding f(x) values. For example, when x=0, f(0)=0+10=10. When x=−10, f(−10)=−10+10=0. When x=5, f(5)=5+10=15.
Step 3: Plot the Points and Draw the Line
Plot the calculated points (−10,0), (0,10), and (5,15) on a coordinate plane. Since it's a linear function, connect these points with a straight line and extend it in both directions to represent the domain R.