Name:__________ warm-up 6-3

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Name:__________ warm-up 6-3 Find the inverse of {(4, 3), (8, 0), (–5, 6)}. Find the inverse of f(x) = x + 3.

Find the inverse of f(x) = 2x – 1. Determine whether the pair of functions are inverse functions. Write yes or no. f(x) = x + 7 g(x) = x – 7 Determine whether the pair of functions are inverse functions. Write yes or no. f(x) = 3x + 4 g(x) = x – 4

Which of the following functions has an inverse that is also a function? A. f(x) = x2 + 3x – 2 B. g(x) = x3 – 8 C. h(x) = x5 + x2 – 4x D. k(x) = 2x2

Details of the Day Activities: EQ: How do radical functions model real-world problems and their solutions? How are expressions involving radicals and exponents related? I will be able to… Activities: Warm-up Review homework Notes: Inverse Functions and Relations Class work/ HW Quiz 6-1 and 6-2 tomorrow Vocabulary: square root function radical function square root inequality Graph and analyze square root functions. . Graph square root inequalities.

6-3 Square Root Functions and Inequalities

A Quick Review Find the inverse of {(4, 3), (8, 0), (–5, 6)}. Find the inverse of f(x) = x + 3.

A Quick Review Find the inverse of f(x) = 2x – 1. Determine whether the pair of functions are inverse functions. Write yes or no. f(x) = x + 7 g(x) = x – 7

A Quick Review Which of the following functions has an inverse that is also a function? A. f(x) = x2 + 3x – 2 B. g(x) = x3 – 8 C. h(x) = x5 + x2 – 4x D. k(x) = 2x2

Notes and examples

Notes and examples

Notes and examples

Notes and examples

Notes and examples

Notes and examples

Notes and examples

Notes and examples A. PHYSICS When an object is spinning in a circular path of radius 2 meters with velocity v, in meters per second, the centripetal acceleration a, in meters per second squared, is directed toward the center of the circle. The velocity v and acceleration a of the object are related by the function . Graph the function in the domain {a|a ≥ 0}.

Notes and examples What would be the centripetal acceleration of an object spinning along the circular path with a velocity of 4 meters per second? It appears from the graph that the acceleration would be 8 meters per second squared. Check this estimate Original equation Replace v with 4. Square each side. Divide each side by 2.

Notes and examples A. GEOMETRY The volume V and surface area A of a soap bubble are related by the function Which is the graph of this function? B. GEOMETRY The volume V and surface area A of a soap bubble are related by the function What would the surface area be if the volume was 3 cubic units?

Notes and examples Graph

Notes and examples