11. Modeling with Functions

11.01 Review: Relations and functions

11.02 Function families and transformations

11.03 Choosing appropriate models

11.04 Domain and range and continuity

11.05 Characteristics from a graph

11.06 Average rates of change

11.07 Comparing function types

11.08 Solutions from a graph

11.09 Operations with functions

11.10 Inverse relations and functions

11.11 Applications of quadratic functions

Investigation: Sine waves and music

Investigation: Modeling tsunami movement

11.12 Fitting functions to quadratic data

United States of America UT

Math III

11.02 Function families and transformations

Interactive practice questions

How do we shift the graph of $y=f\left(x\right)$y=f(x) to get the graph of $y=f\left(x\right)+4$y=f(x)+4?

Move the graph up by $4$4 units.

A

Move the graph down by $4$4 units.

B

Easy

< 1min

How do we shift the graph of $y=g\left(x\right)$y=g(x) to get the graph of $y=g\left(x+6\right)$y=g(x+6)?

Easy

< 1min

Consider the equation $y=4x$y=4x.

Easy

< 1min

The function $y=-5x^2$y=−5x2 has what dilation factor?

Easy

< 1min

Outcomes

III.F.BF.3

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Note the effect of multiple transformations on a single function and the common effect of each transformation across function types. Include functions defined only by a graph. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

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