Lesson 1

Matching up to Data

  • Let’s describe how to transform graphs.

Problem 1

Describe a transformation that gives the graph representing \(g\) from the graph representing \(f\).

a.

Graph of two polynomial functions on x y plane. 

b.

Graph of two polynomial functions on x y plane. 

c.

Graph of two quadratic functions on x y plane. 

 

Problem 2

Describe a way to transform each graph so that it goes through the labeled points.

a.

Graph of a cubic polynomial function, x y plane, and a point at (negative 1 comma 1).

b.

Graph of a exponential function, x y plane, starts near x-axis, goes through (0 comma 1) and keeps growing. A point at (negative 1 comma 0).

c.

Graph of a quadratic function on x y plane, y = x^2, and a point at (2 comma negative 4).

d.

Graph of a function.

Problem 3

Describe a way to transform each graph so that it better matches the data.

a.

Graph of a function.

b.

Graph of two inverse functions on x y plane. 

c.

Graph of two quadratic functions on x y plane. 

 

Problem 4

Does the function \(f\) or the function \(g\) fit the data better? Explain your reasoning.

two functions and data on x y coordinate plane.

Problem 5

For the polynomial function \(A(x)=2x^3+5x^2-28x-15\) we know \((x+5)\) is a factor. Rewrite \(A(x)\) as a product of linear factors.

(From Unit 2, Lesson 13.)