Chapter 3 Flashcard Review

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce. For example, if a function has outputs between -3 and 4, the range is -3 ≤ y ≤ 4.

Front

What does it mean for a relation to be a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). This can be tested using the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is an x-intercept?

Back

The x-intercept of a graph is the point where the graph crosses the x-axis. At this point, the y-coordinate is 0. For example, the x-intercept (-2, 0) means the graph crosses the x-axis at x = -2.

Front

How do you evaluate a function at a specific value?

Back

To evaluate a function at a specific value, substitute the value into the function's equation. For example, for g(x) = 4x - 7, to find g(-9), substitute -9 for x: g(-9) = 4(-9) - 7 = -36 - 7 = -43.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, as the x-values increase, the y-values decrease. For example, if a function is decreasing for x < -1, it means that as x moves left of -1, the function's output values are getting smaller.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If any vertical line drawn through the graph intersects it at more than one point, the graph does not represent a function.

Front

What is the horizontal line test?

Back

The horizontal line test is used to determine if a function is one-to-one. If any horizontal line intersects the graph at more than one point, the function is not one-to-one.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope of a line?

Back

The slope of a line measures its steepness and direction. It is calculated as the change in y divided by the change in x (rise/run). A positive slope means the line rises, while a negative slope means it falls.

Front

What is a y-intercept?

Back

The y-intercept of a graph is the point where the graph crosses the y-axis. At this point, the x-coordinate is 0. For example, in the equation y = 2x + 3, the y-intercept is (0, 3).