Unit 1 Key Features of Graphs

Front

What is the definition of an increasing interval in a graph?

Back

An increasing interval is a range of x-values where the function's output (y-values) rises as x increases.

Front

How do you find the value of a function at a specific point?

Back

To find the value of a function at a specific point, substitute the x-value into the function's equation and solve for f(x).

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What does it mean to reflect a graph over the y-axis?

Back

Reflecting a graph over the y-axis means that for every point (x, y) on the graph, there is a corresponding point (-x, y).

Front

What is a vertical stretch in graph transformations?

Back

A vertical stretch occurs when the y-values of a function are multiplied by a factor greater than 1, making the graph taller.

Front

What does shifting a graph down by 4 units entail?

Back

Shifting a graph down by 4 units means subtracting 4 from the y-values of all points on the graph.

Front

What is the transformation rule for g(x) = f(x-3) + 5?

Back

The transformation rule indicates that the graph of f(x) is shifted right by 3 units and up by 5 units.

Front

How do you determine the intervals of increase on a graph?

Back

To determine intervals of increase, identify where the slope of the graph is positive (rising) between x-values.

Front

What is the effect of a negative sign in front of a function?

Back

A negative sign in front of a function reflects the graph over the x-axis.

Front

What does it mean for a function to be defined on the interval [1, ∞)?

Back

It means that the function is valid for all x-values starting from 1 and extending to positive infinity.