Let $\mathbf{R}$ be the set of real numbers. Define the real function $$f: \mathbf{R} \rightarrow \mathbf{R} \text { by } f(x)=x+10$$ and sketch the graph of this function.

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 $\mathbf{R}$.

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