HW - 4.11 Transformations of Linear Functions

Front

What is a horizontal stretch in the context of linear functions?

Back

A horizontal stretch occurs when the function is transformed to g(x) = f(kx) where 0 < k < 1, making the graph wider.

Front

What is the 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

What does the linear parent function f(x) = x represent?

Back

The linear parent function represents the simplest form of a linear function, with a slope of 1 and a y-intercept of 0.

Front

What transformation is represented by g(x) = -f(x) - 3?

Back

This transformation reflects the graph of f(x) across the x-axis and shifts it down 3 units.

Front

If f(x) = 6x + 8 and g(x) = 6(x + 2) + 8, what transformation occurred?

Back

The function g(x) is a horizontal translation of f(x) to the left by 2 units.

Front

How does multiplying a function by a factor greater than 1 affect its graph?

Back

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

Front

What is the effect of adding a constant to a function?

Back

Adding a constant to a function results in a vertical shift of the graph; if the constant is positive, the graph shifts up, and if negative, it shifts down.

Front

What does a negative coefficient in front of a function indicate?

Back

A negative coefficient indicates a reflection of the graph across the x-axis.

Front

What is the significance of the slope in a linear function?

Back

The slope indicates the rate of change of the function; it represents how much y changes for a unit change in x.

Front

What does the term 'translation' mean in the context of transformations?

Back

Translation refers to shifting the graph of a function horizontally or vertically without changing its shape.