Graph Transformations and Function Notation

The video tutorial covers graph transformations, explaining how changes to function equations affect graph coordinates. It provides examples of transformations, such as translations and reflections, and discusses how to sketch these changes. The tutorial emphasizes understanding the effects of placing numbers inside or outside function brackets and offers practice questions to reinforce learning.

What is the primary focus of graph transformations?

• Altering the position of the graph

• Changing the shape of the graph

• Modifying the color of the graph

• Adjusting the size of the graph

In function notation, what does f(x) represent?

• A specific point on the graph

• The slope of the graph

• The equation of the graph

• The y-intercept of the graph

How does adding a number inside the function bracket affect the x-coordinate?

• It adds the number to the x-coordinate

• It subtracts the number from the x-coordinate

• It multiplies the x-coordinate by the number

• It divides the x-coordinate by the number

What happens to the y-coordinate when a number is added outside the function bracket?

• The y-coordinate is multiplied by the number

• The y-coordinate is divided by the number

• The y-coordinate is increased by the number

• The y-coordinate is decreased by the number

If f(x) is transformed to f(x+3), what happens to the graph?

• The graph shifts 3 units down

• The graph shifts 3 units to the left

• The graph shifts 3 units up

• The graph shifts 3 units to the right

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

• It reflects the graph over the x-axis

• It reflects the graph over the y-axis

• It shifts the graph upwards

• It shifts the graph downwards

How does the transformation f(-x) affect the graph?

• It reflects the graph over the y-axis

• It reflects the graph over the x-axis

• It shifts the graph to the left

• It shifts the graph to the right

What is the result of the transformation y = -f(x)?

• The graph is reflected over the y-axis

• The graph is reflected over the x-axis

• The graph is shifted downwards

• The graph is shifted upwards

When sketching a graph, what is the first step in applying transformations?

• Determine the slope

• Locate whole number coordinates

• Identify the y-intercept

• Find the x-intercept

What does the transformation f(x) + 2 do to the graph?

• Shifts the graph 2 units up

• Shifts the graph 2 units down

• Shifts the graph 2 units to the right

• Shifts the graph 2 units to the left