The given function is:

$f(x) = 3x + 5$

This is a linear function where:

• The slope (rate of change) is 3.
• The y-intercept (the value of $f(x)$ when $x = 0$) is 5.

Key points of the function:

1. Slope: $3$, which means for every unit increase in $x$, the function value $f(x)$ increases by 3.
2. Y-intercept: $5$, which means the line crosses the y-axis at $(0, 5)$.
3. General behavior: Since the slope is positive, the line is increasing, meaning it rises as you move from left to right on the graph.

Would you like to graph this function or explore its properties further?

Related Questions:

1. How do you find the slope and y-intercept of a linear function?
2. How does the slope affect the graph of a linear equation?
3. How do you solve $f(x) = 0$ for this function?
4. What is the domain and range of this function?
5. How would you find the value of $f(x)$ at a specific point, say $x = 2$?

Tip:

For any linear function of the form $f(x) = mx + b$, the coefficient $m$ is the slope, and $b$ is the y-intercept.