Review Midterm precalculus

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is y = x².

Front

How do you find the composition of functions, specifically q(p(-2)) for p(x) = 3x + 4 and q(x) = 2x²?

Back

First, find p(-2): p(-2) = 3(-2) + 4 = -6. Then, substitute -6 into q: q(-6) = 2(-6)² = 72.

Front

What is a piecewise function?

Back

A piecewise function is a function defined by multiple sub-functions, each applying to a certain interval of the main function's domain.

Front

How can you determine if a function is even, odd, or neither?

Back

A function f(x) is even if f(-x) = f(x), odd if f(-x) = -f(x), and neither if it does not satisfy either condition.

Front

What is the result of f(x) - g(x) for f(x) = x² + 9 and g(x) = x - 9?

Back

f(x) - g(x) = (x² + 9) - (x - 9) = x² - x + 18.

Front

What is the definition of a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c.

Front

What does the graph of y = |x| look like?

Back

The graph of y = |x| is a V-shaped graph that opens upwards, intersecting the origin.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, representing the maximum or minimum value of the function.

Front

How do you identify the x-intercepts of a quadratic function?

Back

To find the x-intercepts, set f(x) = 0 and solve for x.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex.