Module 4 Test Remediation

Front

What is the end behavior of the polynomial function f(x) = 2x^2 + 6x^5 + 10x?

Back

Left side: Falls, Right side: Rises.

Front

What are the zeros of the polynomial y = 3(x + 4)(x + 1)(x - 3)?

Back

The zeros are -4, -1, and 3.

Front

How do you identify the lowest relative minimum on a graph?

Back

The lowest relative minimum is the point where the function value is lower than all nearby points. For example, in the given graph, it is -32.

Front

What does it mean for a function to be increasing on an interval?

Back

A function is increasing on an interval if, as x increases, the function value f(x) also increases.

Front

Identify the relative minimum for the graph shown at the point (2, -34).

Back

The relative minimum is the lowest point in the vicinity of (2, -34).

Front

What is the significance of the leading coefficient in a polynomial function?

Back

The leading coefficient determines the end behavior of the polynomial. If positive, the right side rises; if negative, the right side falls.

Front

How do you determine the intervals of increase and decrease for a polynomial function?

Back

By analyzing the first derivative of the function. If f'(x) > 0, the function is increasing; if f'(x) < 0, it is decreasing.

Front

What is a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n are constants and n is a non-negative integer.

Front

What is the degree of a polynomial, and why is it important?

Back

The degree of a polynomial is the highest power of x in the polynomial. It determines the number of zeros and the end behavior of the graph.

Front

What are critical points in the context of polynomial functions?

Back

Critical points are values of x where the first derivative is zero or undefined, indicating potential relative maxima or minima.