REVIEW Mid Unit 5 Algebraic Methods

Front

What is the x-intercept of a function?

Back

The x-intercept of a function is the point where the graph of the function crosses the x-axis, meaning the value of y is zero.

Front

What is the y-intercept of a function?

Back

The y-intercept of a function is the point where the graph of the function crosses the y-axis, meaning the value of x is zero.

Front

How do you find the x-intercept of a linear function f(x) = mx + b?

Back

Set f(x) = 0 and solve for x: 0 = mx + b, which gives x = -b/m.

Front

How do you find the y-intercept of a linear function f(x) = mx + b?

Back

The y-intercept is the value of f(0), which is b.

Front

What is the relationship between the x-intercepts of the product of two functions?

Back

The x-intercepts of k(x) = f(x) * g(x) are the x-intercepts of f(x) and g(x) combined.

Front

What is the formula for the volume of a cylinder?

Back

The volume V of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height.

Front

If the diameter of a cylinder is d, what is the radius?

Back

The radius r is half of the diameter: r = d/2.

Front

Given a cylinder with diameter 6x, what is the radius?

Back

The radius r is 3x, since r = d/2 = 6x/2.

Front

How do you calculate the volume of a cylinder with radius r and height h?

Back

Use the formula V = πr²h.

Front

What is the volume of a cylinder with radius 3x and height x + 5?

Back

V = π(3x)²(x + 5) = 27πx²(x + 5) = 27πx³ + 135πx².