Linear Function 38520E

1. **State the problem:** We are given the function $$f(x) = 3x + 1$$ and we want to understand or analyze it. 2. **Formula and explanation:** This is a linear function of the form $$f(x) = mx + b$$ where $$m$$ is the slope and $$b$$ is the y-intercept. 3. **Identify slope and intercept:** Here, the slope $$m = 3$$ and the y-intercept $$b = 1$$. 4. **Interpretation:** The slope $$3$$ means for every increase of 1 in $$x$$, $$f(x)$$ increases by 3. 5. **Find intercepts:** - To find the y-intercept, set $$x=0$$: $$f(0) = 3(0) + 1 = 1$$. - To find the x-intercept, set $$f(x) = 0$$: $$0 = 3x + 1$$ $$3x = -1$$ $$x = \frac{-1}{3}$$ 6. **Summary:** The function is a straight line with slope 3, crossing the y-axis at 1 and the x-axis at $$-\frac{1}{3}$$.