EOC Checkpoint 1 - Equations and Transformations

Front

What is a horizontal shift in a graph?

Back

A horizontal shift occurs when the graph of a function is moved left or right along the x-axis. For example, g(x) = (x - 7.5)² represents a horizontal shift of 7.5 units to the right from f(x) = x².

Front

What does a vertical shift in a graph mean?

Back

A vertical shift occurs when the graph of a function is moved up or down along the y-axis. For example, g(x) = x² + 4 represents a vertical shift of 4 units up from f(x) = x².

Front

How do you represent a horizontal shift to the left in a function?

Back

A horizontal shift to the left is represented by adding a positive value inside the function. For example, g(x) = (x + 4.5)² represents a shift of 4.5 units to the left from f(x) = x².

Front

What is a reflection over the x-axis?

Back

A reflection over the x-axis occurs when the graph of a function is flipped upside down. For example, h(x) = -f(x) reflects the graph of f(x) over the x-axis.

Front

What is a reflection over the y-axis?

Back

A reflection over the y-axis occurs when the graph of a function is flipped horizontally. For example, h(x) = f(-x) reflects the graph of f(x) over the y-axis.

Front

What is a vertical stretch in a graph?

Back

A vertical stretch occurs when the graph of a function is stretched away from the x-axis. For example, g(x) = 2f(x) stretches the graph of f(x) vertically by a factor of 2.

Front

What is a horizontal stretch in a graph?

Back

A horizontal stretch occurs when the graph of a function is stretched away from the y-axis. For example, g(x) = f(0.5x) stretches the graph of f(x) horizontally by a factor of 2.

Front

How do you solve the equation 8x - 3(2x - 4) = 3(x - 6)?

Back

First, distribute: 8x - 6x + 12 = 3x - 18. Combine like terms: 2x + 12 = 3x - 18. Then, isolate x: 30 = x, so the solution is x = 30.

Front

What is the solution to the equation 4(0.5n - 3) = n - 0.25(12 - 8n)?

Back

Distributing gives: 2n - 12 = n - 3 + 2n. Combine like terms: -12 = 3n - 3. Solving gives n = -9.

Front

What does it mean to translate a graph?

Back

Translating a graph means shifting it in a specific direction without changing its shape. For example, translating f(x) = x² 4.5 units to the left results in g(x) = (x + 4.5)².