Flashcard 3.7 - 3.10 Quiz Prep

Front

What is a transformation in the context of graphing functions?

Back

A transformation refers to a change in the position, size, or shape of a graph. Common transformations include translations (shifts), reflections, stretches, and compressions.

Front

How does a vertical shift affect the graph of a function?

Back

A vertical shift moves the graph up or down without changing its shape. For example, if f(x) is shifted up by 3 units, the new function is g(x) = f(x) + 3.

Front

What does it mean for a graph to be 'steeper' or 'flatter'?

Back

A graph is 'steeper' if it rises or falls more sharply, which corresponds to a larger absolute value of the slope. A 'flatter' graph rises or falls more gradually, indicating a smaller absolute value of the slope.

Front

What is slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

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 is the effect of multiplying a function by a factor greater than 1?

Back

Multiplying a function by a factor greater than 1 results in a vertical stretch of the graph, making it steeper.

Front

What is the effect of multiplying a function by a factor between 0 and 1?

Back

Multiplying a function by a factor between 0 and 1 results in a vertical compression of the graph, making it flatter.

Front

What does it mean for a graph to be reflected over the x-axis?

Back

A reflection over the x-axis means that for every point (x, y) on the graph, the corresponding point on the reflected graph is (x, -y).

Front

What is the transformation of the parent function f(x) = x to g(x) = 3x + 5?

Back

The transformation involves a vertical shift up by 5 units and a vertical stretch, making the graph steeper.

Front

How do you determine if a graph has been shifted left or right?

Back

A graph is shifted left by h units if the function is in the form f(x + h) and shifted right if it is in the form f(x - h).