Linear parent function f is graphed on the grid.
Which graph best represents g(x)= 2f(x)-5?
Linear parent function f is graphed on the grid.
Which graph best represents g(x)= 2f(x)-5?
It looks like your question is missing the actual graphical depiction of the linear parent function f. Without actually seeing the graph of the function f, I can only provide a general explanation of what to look for in selecting the graph that would represent the transformation applied to f, that is g(x) = 2f(x) - 5.
Here is what you'd expect to see in the graph of g(x) = 2f(x) - 5 assuming you start with a basic linear parent function f(x) = x:
1. Scaling by 2: The function f(x) is multiplied by 2, so all the y-values are doubled relative to the y-values of f(x). The slope of the line would become steeper if it were positive, and shallower if it were negative — but since it's a parent function, it generally has a slope of 1, and doubling it would result in a slope of 2.
2. Vertical shift by -5: After scaling the function by 2, you then subtract 5 from all the y-values which shifts the entire graph down by 5 units.
The new function g(x) would still be linear, and hence its graph would also be a straight line. To find the appropriate graph of g(x), you would need to identify a graph where the line is twice as steep compared to the original line representing f(x) and is shifted downwards so that every point on the line is 5 units lower than it would have been before the transformations.
Given an actual graph of f(x), you could perform these transformations point by point; however, without any images attached to your question, it is impossible to give a definitive answer about which graph represents g(x) = 2f(x) - 5. If you have a specific graph of f(x) in mind or an image, please share it so we can give you a more precise response.
is the graph more vertical or horisantal
Given the function g(x) = 2f(x) - 5, where f(x) is the linear parent function (usually f(x) = x), we can infer some characteristics of the graph of g(x):
Since f(x) is a linear function with a slope of 1 (if we assume f(x) = x) and no y-intercept (it passes through the origin), the modification applied to f(x) to obtain g(x) involves:
1. A scaling factor of 2: This will cause the graph of g(x) to be steeper than the graph of f(x). The slope of g(x) will be twice the slope of f(x). So if f(x) had a slope of 1 (45-degree angle), g(x) will have a slope of 2, making it more vertical than the graph of f(x).
2. A vertical shift down 5 units: This shifts the entire graph of f(x) down by 5 units but does not change the slope of the line. It changes the y-intercept but does not affect the orientation of the graph in terms of it being more vertical or horizontal.
In summary, the graph of g(x) will be more vertical than the graph of f(x) due to the scaling factor. It is also important to note that regardless of more vertical or horizontal, the graph of a linear function is always a straight line. The terms "vertical" or "horizontal" when used here are relative: all non-horizontal lines could be described as "more vertical" if their slope increases, and "more horizontal" if their slope decreases.
To find the graph that represents g(x) = 2f(x) - 5, you need to understand how the equation transforms the parent function f(x).
The parent function, f(x), is a linear function with a slope of 1 and a y-intercept of 0. It is a straight line that passes through the origin of the graph.
When we add 2f(x), it means that we are vertically stretching the function by a factor of 2. This means that each point on the graph of f(x) will move upward, becoming twice as high as before.
Finally, when we subtract 5, it means that we are shifting the entire graph downward by 5 units.
Given this information, you can now determine which graph best represents g(x) = 2f(x) - 5 by observing the transformations described above. Look for the graph that has a vertical stretch by a factor of 2 compared to the parent function, and then shifted downward by 5 units.
Please refer to the provided graphs to determine which one satisfies these conditions and best represents g(x) = 2f(x) - 5.