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4.07 Function composition

Adaptive
Worksheet

Interactive practice questions

Consider the graph of the function $f\left(x\right)$f(x).

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A Coordinate Plane with both its x- and y-axes ranging from $-7$7 to $7$7. Both axes are marked with intervals of $1$1. A downward facing parabola if plotted on the Coordinate Plane. The vertex of the parabola is located at $\left(3,4\right)$(3,4). The parabola also passes through a point $3$3 units vertically from the x-axis where $x=2$x=2. The point is not marked and not explicitly labeled.

What is $f\left(2\right)$f(2)?

Easy
< 1min

Consider the graph of the function $f\left(x\right)$f(x).

Easy
< 1min

The piecewise function $h\left(x\right)$h(x) is shown below:

Easy
< 1min

The piecewise function $f\left(x\right)$f(x) is shown below:

Easy
< 1min
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Outcomes

A2.F.2

The student will investigate and analyze characteristics of square root, cube root, rational, polynomial, exponential, logarithmic, and piecewise-defined functions algebraically and graphically.

A2.F.2f

For any value, x, in the domain of f, determine f(x) using a graph or equation. Explain the meaning of x and f(x) in context, where applicable.

A2.F.2k

Determine the composition of two functions algebraically and graphically.

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