Question

Q1: A linear function is given.

g(x) = −5x + 9

(a) Find the average rate of change of the function between
x = a and x = a + h.

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Q2: A function f is given, and the indicated transformation is applied to its graph. Write the equation for the final transformed graph.
f(x) = √x; shift 3 units to the left

y =

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Q3: Find f ∘ g ∘ h.
f(x) = x − 6, g(x) = √x, h(x) = x − 6

Answer 1

Q1: as always, it is just the slope of the line joining the two points on the graph:
[g(a+h) - g(a)]/h = [(-5(a+h)+9) - (-5a+9)]/h = -5h/h = -5

Q2: y = √(x+3)
review shifting

Q3: f∘g = f(g) = g-6 = √x - 6
f∘h = h-6 = x-6 - 6 = x-12
g∘h = √h = √(x-6)
(f∘g)∘h = √h - 6 = √(x-6) - 6
f∘(g∘h) = √(x-6) - 6
Note that composition is associative so f∘g∘h is unambiguous

Answer 2

thanks for the answers but I wasn't able to understand Question 1 answer can u please explain it?

Answer 3

review slopes. The slope is ∆y/∆x
The average rate of change is the constant slope between two points on the graph. The graph may curve, so the slope will change from point to point. But the slope of the secant line is the constant rate of change that accomplishes the same thing.