Graph Transformations and Function Evaluation

The video tutorial covers various mathematical concepts that will be tested, including plotting points on a coordinate plane, graphing different types of functions, evaluating and performing operations on functions, determining if functions are even, odd, or neither, finding the domain of functions, and sketching graph transformations. The teacher provides detailed explanations and examples for each topic to prepare students for the upcoming test.

What is the first step in plotting a point on a coordinate plane?

• Draw the axes

• Determine the y-coordinate

• Determine the x-coordinate

• Identify the quadrant

Which quadrant does the point (2, -7) lie in?

How do you find the slope of a line when graphing?

• By solving for x

• By dividing the change in y by the change in x

• By finding the y-intercept

• By using the midpoint formula

What is the center of a circle with the equation x^2 + y^2 = 9?

• (0, 0)

• (3, 3)

• (9, 9)

• (1, 1)

How do you determine which part of a circle to graph from the equation x = sqrt(9 - y^2)?

• By solving for y

• By using the center of the circle

• By checking if x or y is squared

• By finding the radius

What is the vertex of a parabola with the equation y = (x - 4)^2 + 5?

• (5, 4)

• (4, 0)

• (4, 5)

• (0, 0)

How do you evaluate a function at a specific point?

• By graphing the function

• By substituting the point into the function

• By finding the derivative

• By solving for x

What is the result of adding two functions f(x) and g(x)?

• f(x) * g(x)

• f(x) - g(x)

• f(x) + g(x)

• f(x) / g(x)

How can you determine if a function is even?

• If it reflects over the y-axis

• If it reflects over the x-axis

• If it reflects over the origin

• If it is symmetric about the line y = x

What is the domain of a function with a denominator of x^2 - 16?

• All real numbers

• All real numbers except x = ±4

• All real numbers except x = 0

• All real numbers except x = 16