Functions and SLope

Front

What is a transformation in the context of graph functions?

Back

A transformation refers to a change in the position, size, or shape of a graph, which can include translations, reflections, stretches, and compressions.

Front

What does a vertical translation of a graph entail?

Back

A vertical translation moves the graph up or down without changing its shape.

Front

How does adding a constant to a function affect its graph?

Back

Adding a constant to a function shifts the graph vertically. For example, f(x) + c shifts the graph up by c units if c is positive and down by c units if c is negative.

Front

What is the effect of subtracting a constant from a function on its graph?

Back

Subtracting a constant from a function shifts the graph vertically down. For example, f(x) - c shifts the graph down by c units.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that the line is decreasing, meaning as x increases, y decreases.

Front

What is the transformation when f(x) = x is replaced with f(x) + 2?

Back

This transformation results in a vertical translation of the graph up by 2 units.

Front

What is the transformation when f(x) is replaced with f(x) - 4?

Back

This transformation results in a vertical translation of the graph down by 4 units.

Front

What is the effect of multiplying a function by a negative number?

Back

Multiplying a function by a negative number reflects the graph across the x-axis.