suppose the graph of f is given . Describe how the graph of the function can be obtained from the graph of f . Y = 4f ( x + 5 )- 3 .
How would I work this problem?
I assume you have a graph of f(x) and you want a graph of 4 f(x+5)^-3. Call that new function g(x). I assume you want a value of the new function g(x) at x.
(1) See what the value of f(x) was at x+5, using the graph of f(x)
(2) Raise that f(x+5) value to the -3 power
(3) Multiply the result by 4.
(4) Plot the g(x) point and continue the process with other points.
se the equation
y
= 3.5
x
to answer the questions.
(a)
What is the slope of
y
= 3.5
x
and what does this mean?
(Use at least one complete sentence to
explain your answer.)
(b)
What is the y
-
intercept?
(Use at least one complete sentence to explain your answer.)
(c)
Make
up
a story that can be represented by
y
= 3.5
x
.
(Use at l
east two complete sentences to explain your answer)
To obtain the graph of the function y = 4f(x + 5) - 3 from the given graph of f, you need to follow these steps:
Step 1: Start with the given graph of f.
Step 2: Make a horizontal shift of 5 units to the left. This means that every point (x, y) on the original graph of f will be shifted 5 units to the left, resulting in a new point (x + 5, y).
Step 3: Stretch the graph vertically by a factor of 4. This means that the y-coordinate of every point will be multiplied by 4, resulting in a new point (x + 5, 4y).
Step 4: Shift the graph downward by 3 units. This means that the y-coordinate of every point will be decreased by 3, resulting in a new point (x + 5, 4y - 3).
Step 5: Plot the new points obtained from Steps 2, 3, and 4 on a coordinate plane.
Step 6: Connect the plotted points to obtain the graph of the function y = 4f(x + 5) - 3.
Please note that these steps assume that the original graph of f is continuous and doesn't have any discontinuities or asymptotes.
To obtain the graph of the function Y = 4f(x + 5) - 3 from the given graph of f(x), you can follow these steps:
1. Start with the original graph of f(x).
2. Shift the graph horizontally by 5 units to the left. This can be done by replacing x in the equation with (x + 5). This shift will move all the points on the graph of f(x) horizontally 5 units to the left.
3. Stretch the graph vertically by a factor of 4. Multiply every y-coordinate by 4 to achieve this stretch. This will vertically exaggerate the y-values of the graph.
4. Finally, shift the graph downwards by 3 units. This can be done by subtracting 3 from every y-coordinate of the graph. This shift will move the entire graph downwards.
By following these steps, you will obtain the graph of the function Y = 4f(x + 5) - 3, which is a transformation of the original graph of f(x).