Exploring Graphing Functions

The video tutorial covers graphing basic functions, focusing on linear and quadratic functions. It explains how to graph a linear function with a slope of 1 and a y-intercept of 0, and how adding a constant shifts the graph vertically. The tutorial also covers graphing a quadratic function, highlighting how multiplying by a constant affects the parabola's width and how subtracting a constant shifts it vertically. The video emphasizes understanding function shifts by adding or subtracting values, which moves the graph up or down.

What is the slope of the line represented by the function f(x) = x?

• 2

• 1

• -1

• 0

Where does the line f(x) = x intersect the y-axis?

• At y = 2

• At y = -1

• At y = 1

• At y = 0

How does the graph of y = x + 1 compare to the graph of y = x?

• It is shifted up by 1 unit.

• It is shifted down by 1 unit.

• It is shifted right by 1 unit.

• It is shifted left by 1 unit.

What is the new y-intercept of the graph y = x + 1?

• 2

• -1

• 1

• 0

What type of function is represented by f(x) = 3x^2?

• Linear

• Quadratic

• Exponential

• Cubic

How does the coefficient 3 affect the parabola of the function f(x) = 3x^2?

• It makes the parabola wider.

• It shifts the parabola down.

• It makes the parabola narrower.

• It shifts the parabola up.

What happens to the graph of f(x) = 3x^2 when we subtract 2 from it?

• It shifts left by 2 units.

• It shifts up by 2 units.

• It shifts right by 2 units.

• It shifts down by 2 units.

What is the new vertex of the parabola after shifting f(x) = 3x^2 down by 2 units?

• (0, -2)

• (0, 0)

• (0, 2)

• (2, 0)

If the original vertex of the parabola f(x) = 3x^2 is at (0, 0), where is the vertex after shifting it down by 2 units?

• (0, -2)

• (2, 0)

• (0, 0)

• (0, 2)

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

• It changes the slope of the function.

• It changes the y-intercept of the function.

• It shifts the graph up or down.

• It shifts the graph left or right.