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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