Horizontal & Vertical Shifts of Linear Functions

Front

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

Back

A horizontal shift refers to the translation of a function left or right on the graph, determined by the value added or subtracted from the input variable x.

Front

How does the equation g(x) = f(x - c) affect the graph of f(x)?

Back

The equation g(x) = f(x - c) translates the graph of f(x) to the right by c units.

Front

What does the equation g(x) = f(x + c) indicate about the transformation of f(x)?

Back

The equation g(x) = f(x + c) translates the graph of f(x) to the left by c units.

Front

What is a vertical shift in the context of linear functions?

Back

A vertical shift refers to the translation of a function up or down on the graph, determined by the value added or subtracted from the output variable.

Front

How does the equation g(x) = f(x) + k affect the graph of f(x)?

Back

The equation g(x) = f(x) + k translates the graph of f(x) upward by k units if k is positive, and downward by k units if k is negative.

Front

What is the effect of the transformation g(x) = f(x - 3) on the function f(x)?

Back

The transformation g(x) = f(x - 3) shifts the graph of f(x) to the right by 3 units.

Front

If g(x) = f(x - 4) + 6, what transformations are applied to f(x)?

Back

The function f(x) is translated to the right by 4 units and upward by 6 units.

Front

Given f(x) = mx + b, how does the transformation g(x) = f(x) + k change the function?

Back

The transformation g(x) = f(x) + k results in a new function with the same slope m, but the y-intercept is increased by k.

Front

What is the new rule for the function f(x) = 7x + 3 when translated up 6 units?

Back

The new rule is g(x) = 7x + 9.

Front

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

Back

Translation refers to shifting the entire graph of a function in a specific direction without changing its shape.