**How does the graph of g(x) = 3x – 2 compare to the graph of f(x) = 3x?** We’ve left below all the answers you need to know about this topic.

**How does the graph of g(x) = 3x – 2 compare to the graph of f(x) = 3x?**

The functions (g(x) = 3x – 2) and (f(x) = 3x) are both linear functions, meaning they have a constant rate of change. This is because the highest power of (x) in both functions is 1. However, the difference between them lies in the constant term.

**How does the graph of g(x) = 3x – 2 compare to the graph of f(x) = 3x?/ Graph Comparison:**

**Slope:**Both functions have the same slope, which is 3. This means that for every 1 unit increase in (x), the value of the function increases by 3 units. The slope determines how steep the line is.**Y-Intercept:**The main difference between the two functions is the y-intercept. For (f(x) = 3x), the y-intercept is at the origin (0,0), while for (g(x) = 3x – 2), the y-intercept is at (0, -2). This means that (g(x)) is shifted downward by 2 units compared to (f(x)).**Shift:**The function (g(x)) is a vertical shift of (f(x)) by 2 units downward. This vertical shift is due to the constant term -2 in (g(x)).**Intersection with Y-Axis:**The intersection point of (f(x)) with the y-axis is (0,0), while the intersection point of (g(x)) with the y-axis is (0, -2).**Graph Appearance:**Visually, the graph of (g(x)) is obtained by shifting the graph of (f(x)) downward by 2 units. The two lines are parallel, and (g(x)) is always 2 units below (f(x)).**Parallel Lines:**Since both functions have the same slope, their graphs are parallel. Parallel lines have the same steepness but different y-intercepts.

In summary, the graphs of (g(x) = 3x – 2) and (f(x) = 3x) are both straight lines with a slope of 3, but they differ in their y-intercepts. The graph of (g(x)) is obtained by shifting the graph of (f(x)) downward by 2 units. This comparison helps to understand how changes in constants within linear functions affect their graphical representation. How does the graph of g(x) = 3x – 2 compare to the graph of f(x) = 3x? topic is over.

**Summary:**

f(x) = 3x passes through the origin, whereas g(x) = 3x -2 passes through the point (0,-2).

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