Unit 1 Key Features of Graphs

Front

What is the x-intercept?

Back

The x-intercept is the point where the graph intersects the x-axis, represented as (x, 0). For example, (12, 0) is an x-intercept.

Front

What is the domain of a graph?

Back

The domain of a graph is the set of all possible x-values (inputs) for which the function is defined. For example, the domain [1, ∞) includes all x-values from 1 to infinity.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as x increases, the value of the function also increases. For example, the function is increasing on the interval (-∞, 5).

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, as x increases, the value of the function decreases. For example, the function is decreasing from 0 to 3.

Front

What is a vertical compression of a graph?

Back

A vertical compression occurs when the graph of a function is squeezed towards the x-axis. For example, a function f(x) compressed by a factor of 1/2 becomes 1/2 f(x).

Front

What is a horizontal shift in a graph?

Back

A horizontal shift occurs when the graph of a function is moved left or right. For example, f(x - 4) shifts the graph 4 units to the right.

Front

What is a vertical shift in a graph?

Back

A vertical shift occurs when the graph of a function is moved up or down. For example, f(x) + 1 shifts the graph 1 unit up.

Front

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

Back

Reflecting a graph over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

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

Back

A negative coefficient reflects the graph over the x-axis. For example, g(x) = -f(x) reflects f(x) over the x-axis.

Front

How do you determine the x-intercept from a function?

Back

To find the x-intercept, set the function equal to zero and solve for x. For example, if f(x) = 0, find x such that f(x) = 0.