Algebra 2_Unit 1 Topic 3 FA3 Review II

Front

What is a transformation in algebra?

Back

A transformation in algebra refers to the process of changing a function's graph through operations such as translation, dilation, reflection, or rotation.

Front

Define dilation in the context of function transformations.

Back

Dilation is a transformation that stretches or compresses the graph of a function vertically or horizontally, based on a dilation factor.

Front

What does a dilation factor greater than 1 indicate?

Back

A dilation factor greater than 1 indicates a vertical stretch of the graph.

Front

What does a dilation factor between 0 and 1 indicate?

Back

A dilation factor between 0 and 1 indicates a vertical compression of the graph.

Front

How does a horizontal translation affect a function's graph?

Back

A horizontal translation shifts the graph of a function left or right along the x-axis.

Front

What is the average rate of change of a function?

Back

The average rate of change of a function over an interval is the change in the function's value divided by the change in the input value over that interval.

Front

How do you calculate the average rate of change between two points (x1, y1) and (x2, y2)?

Back

Average rate of change = (y2 - y1) / (x2 - x1).

Front

What is the effect of adding a constant to a function's output?

Back

Adding a constant to a function's output results in a vertical translation of the graph.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a * b^x, where a is a constant and b is the base.

Front

What is the base of a logarithmic function?

Back

The base of a logarithmic function is the number that is raised to a power to obtain a given value, represented as log_b(x).