Order the group of quadratic functions from widest to narrowest graph.
1 answer:
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Answer:
1/4
Step-by-step explanation:
The tangent line to f(x) at x=2 goes through the point (2, 8) and has slope 4.
The inverse function f⁻¹(x) is a reflection of the function f(x) across the line y=x. The corresponding tangent line will go through point (8, 2) and have slope 1/f'(2) = 1/4 at that point. That is, ...
(f⁻¹)'(8) = 1/f'(f⁻¹(8)) = 1/f'(2) = 1/4
Hey there!
Linear functions have a continuous change.
Let's check these tables and see if we can tell linear functions from non-linear functions.
The first one is
- x values: -1, 0, 1, 2
- we add 1 each time
- y values: 8, 5, 2, -1
- we subtract 3 each time
Let's try the next one:
- x values: -1, 0, 1, 2
- we add 1 each time
- y values: 5, 10, 15, 20
- we add 5 each time
Let's try the third one:
- x values: -1, 0, 1, 2
- - we add 1 each time
- y values: 15, 18, 20, 21
- we add 3, then 2, then 1..
So this table doesn't represent a linear function.
Let's check the fourth one:
- x values: -1, 0, 1, 2
- we add 1 each time
- y values: 1, 2, 3, 4
- we add 1 each time
Thus, Option C is the right option.
Hope everything is clear.
Let me know if you have any questions!
Always remember: Knowledge is power!