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8.5 Functions and Volume

I can write rules when I know input-output pairs.
I know how an input-output diagram represents a rule.

I know that a function is a rule with exactly one output for each allowable input.
I know that if a rule has exactly one output for each allowable input, then the output depends on the input.

I can find the output of a function when I know the input.
I can name the independent and dependent variables for a given function and represent the function with an equation.

I can identify graphs that do, and do not, represent functions.
I can use a graph of a function to find the output for a given input and to find the input(s) for a given output.

I can explain the story told by the graph of a function.

I can draw the graph of a function that represents a real-world situation.

I can compare inputs and outputs of functions that are represented in different ways.

I can determine whether a function is increasing or decreasing based on whether its rate of change is positive or negative.
I can explain in my own words how the graph of a linear function relates to its rate of change and initial value.

I can decide when a linear function is a good model for data and when it is not.
I can use data points to model a linear function.

I can create graphs of non-linear functions with pieces of linear functions.

I can collect data about a function and represent it as a graph.
I can describe the graph of a function in words.

I know that volume is the amount of space contained inside a three-dimensional figure.
I recognize the 3D shapes cylinder, cone, rectangular prism, and sphere.

I can find the volume of a cylinder in mathematical and real-world situations.
I know the formula for volume of a cylinder.

I can find missing information about a cylinder if I know its volume and some other information.

I can find the volume of a cone in mathematical and real-world situations.
I know the formula for the volume of a cone.

I can find missing information of about a cone if I know its volume and some other information.

I can create a graph the relationship between volume and height for all cylinders (or cones) with a fixed radius.
I can explain in my own words why changing the height by a scale factor changes the volume by the same scale factor.

I can create a graph representing the relationship between volume and radius for all cylinders (or cones) with a fixed height.
I can explain in my own words why changing the radius by a scale factor changes the volume by the scale factor squared.

I can estimate the volume of a hemisphere by calculating the volume of shape I know is larger and the volume of a shape I know is smaller.

I can find the volume of a sphere when I know the radius.

I can find the radius of a sphere if I know its volume.
I can solve mathematical and real-world problems about the volume of cylinders, cones, and spheres.

I can compare functions about volume represented in different ways.