2.1 Practice

Last updated over 2 years ago

19 questions

Check Your Understanding on "Can We Predict Stock Values?"

Check Your Understanding on "What’s Up With the Zeros?"

Check Your Understanding on "Who is the Fairest of Them All?"

2.1 Practice

Last updated over 2 years ago

19 questions

Check Your Understanding on "Can We Predict Stock Values?"

Selected values of a polynomial function f are given.
Determine the degree of the polynomial.

The graph of a quartic polynomial y=f(x) is shown.

Determine the number of x-intercepts of f.

Determine the number of relative minima and relative maxima and label them.
Relative minima: _______ 
Relative maxima:  _______ 

A polynomial function g has x-intercepts at x=0 and x=4. Which of the following statements must be true?

Check Your Understanding on "What’s Up With the Zeros?"

The graph of a 6th degree polynomial y=g(x) is shown.

Identify all the zeros of g and state their multiplicity.

Does the equation g(x)=0 have any imaginary solutions?
How do you know?

A polynomial has zeros at x=4 (with a multiplicity of 2), x=-2, and x=3i.

What is the minimum degree of the polynomial?

Write an equation for the polynomial in factored form.

What if the y-intercept had to be 864?
Write a new equation.

Let f(x)=(x+6)(x^{2}+2x+5).

Find all zeroes of f.

Rewrite the equation for f(x) in fully factored form (only linear factors).

Check Your Understanding on "Who is the Fairest of Them All?"

Half of the graph of an odd function is shown below. Sketch the other half of the function.

If (3,-18) is on the graph of an even function, what other point is guaranteed to be on the graph?

Is y=x^{5}+x^{3}+3 an even function, an odd function, or neither?
Prove your answer algebraically.

True or false: If the statement is true, explain why it must be true using the definitions of even and odd functions. If it is false, provide a counterexample in the Show Your Work tool.

All even functions go through the origin.

True or false: If the statement is true, explain why it must be true using the definitions of even and odd functions. If it is false, provide a counterexample in the Show Your Work tool.

If each term in a polynomial function has an even exponent, the function is even.

2.1 Practice

2.1 Practice

Selected values of a polynomial function f are given.
Determine the degree of the polynomial.

Determine the number of x-intercepts of f.

A polynomial function g has x-intercepts at x=0 and x=4. Which of the following statements must be true?

Identify all the zeros of g and state their multiplicity.

Does the equation g(x)=0 have any imaginary solutions?
How do you know?

What is the minimum degree of the polynomial?

Write an equation for the polynomial in factored form.

What if the y-intercept had to be 864?
Write a new equation.

Find all zeroes of f.

Rewrite the equation for f(x) in fully factored form (only linear factors).

Half of the graph of an odd function is shown below. Sketch the other half of the function.

If (3,-18) is on the graph of an even function, what other point is guaranteed to be on the graph?

Is y=x^{5}+x^{3}+3 an even function, an odd function, or neither?
Prove your answer algebraically.

True or false: If the statement is true, explain why it must be true using the definitions of even and odd functions. If it is false, provide a counterexample in the Show Your Work tool.

All even functions go through the origin.

True or false: If the statement is true, explain why it must be true using the definitions of even and odd functions. If it is false, provide a counterexample in the Show Your Work tool.

If each term in a polynomial function has an even exponent, the function is even.

Selected values of a polynomial function f are given.
Determine the degree of the polynomial.

Determine the number of x-intercepts of f.

How many times does the graph of change concavity?

Label the absolute minimum A, or explain why this value does not exist.

Label the absolute maximum B, or explain why this value does not exist.

A polynomial function g has x-intercepts at x=0 and x=4. Which of the following statements must be true?

Identify all the zeros of g and state their multiplicity.

Does the equation g(x)=0 have any imaginary solutions?
How do you know?

What is the minimum degree of the polynomial?

Write an equation for the polynomial in factored form.

What if the y-intercept had to be 864?
Write a new equation.

Find all zeroes of f.

Rewrite the equation for f(x) in fully factored form (only linear factors).

Half of the graph of an odd function is shown below. Sketch the other half of the function.

If (3,-18) is on the graph of an even function, what other point is guaranteed to be on the graph?

Is y=x^{5}+x^{3}+3 an even function, an odd function, or neither?
Prove your answer algebraically.

True or false: If the statement is true, explain why it must be true using the definitions of even and odd functions. If it is false, provide a counterexample in the Show Your Work tool.

All even functions go through the origin.

True or false: If the statement is true, explain why it must be true using the definitions of even and odd functions. If it is false, provide a counterexample in the Show Your Work tool.

If each term in a polynomial function has an even exponent, the function is even.

How many times does the graph of change concavity?

Label the absolute minimum A, or explain why this value does not exist.

Label the absolute maximum B, or explain why this value does not exist.

2.1 Practice

2.1 Practice

Selected values of a polynomial function f are given. Determine the degree of the polynomial.

Determine the number of x-intercepts of f.

A polynomial function g has x-intercepts at x=0 and x=4. Which of the following statements must be true?

Identify all the zeros of g and state their multiplicity.

Does the equation g(x)=0 have any imaginary solutions? How do you know?

What is the minimum degree of the polynomial?

Write an equation for the polynomial in factored form.

What if the y-intercept had to be 864? Write a new equation.

Find all zeroes of f.

Rewrite the equation for f(x) in fully factored form (only linear factors).

Half of the graph of an odd function is shown below. Sketch the other half of the function.

If (3,-18) is on the graph of an even function, what other point is guaranteed to be on the graph?

Is y=x^{5}+x^{3}+3 an even function, an odd function, or neither? Prove your answer algebraically.

True or false: If the statement is true, explain why it must be true using the definitions of even and odd functions. If it is false, provide a counterexample in the Show Your Work tool.All even functions go through the origin.

True or false: If the statement is true, explain why it must be true using the definitions of even and odd functions. If it is false, provide a counterexample in the Show Your Work tool.If each term in a polynomial function has an even exponent, the function is even.

Selected values of a polynomial function f are given. Determine the degree of the polynomial.

Determine the number of x-intercepts of f.

How many times does the graph of change concavity?

Label the absolute minimum A, or explain why this value does not exist.

Label the absolute maximum B, or explain why this value does not exist.

A polynomial function g has x-intercepts at x=0 and x=4. Which of the following statements must be true?

Identify all the zeros of g and state their multiplicity.

Does the equation g(x)=0 have any imaginary solutions? How do you know?

What is the minimum degree of the polynomial?

Write an equation for the polynomial in factored form.

What if the y-intercept had to be 864? Write a new equation.

Find all zeroes of f.

Rewrite the equation for f(x) in fully factored form (only linear factors).

Half of the graph of an odd function is shown below. Sketch the other half of the function.

If (3,-18) is on the graph of an even function, what other point is guaranteed to be on the graph?

Is y=x^{5}+x^{3}+3 an even function, an odd function, or neither? Prove your answer algebraically.

True or false: If the statement is true, explain why it must be true using the definitions of even and odd functions. If it is false, provide a counterexample in the Show Your Work tool.All even functions go through the origin.

True or false: If the statement is true, explain why it must be true using the definitions of even and odd functions. If it is false, provide a counterexample in the Show Your Work tool.If each term in a polynomial function has an even exponent, the function is even.

How many times does the graph of change concavity?

Label the absolute minimum A, or explain why this value does not exist.

Label the absolute maximum B, or explain why this value does not exist.

Selected values of a polynomial function f are given.
Determine the degree of the polynomial.

Does the equation g(x)=0 have any imaginary solutions?
How do you know?

What if the y-intercept had to be 864?
Write a new equation.

Is y=x^{5}+x^{3}+3 an even function, an odd function, or neither?
Prove your answer algebraically.

True or false: If the statement is true, explain why it must be true using the definitions of even and odd functions. If it is false, provide a counterexample in the Show Your Work tool.

All even functions go through the origin.

True or false: If the statement is true, explain why it must be true using the definitions of even and odd functions. If it is false, provide a counterexample in the Show Your Work tool.

If each term in a polynomial function has an even exponent, the function is even.

Selected values of a polynomial function f are given.
Determine the degree of the polynomial.

Does the equation g(x)=0 have any imaginary solutions?
How do you know?

What if the y-intercept had to be 864?
Write a new equation.

Is y=x^{5}+x^{3}+3 an even function, an odd function, or neither?
Prove your answer algebraically.

True or false: If the statement is true, explain why it must be true using the definitions of even and odd functions. If it is false, provide a counterexample in the Show Your Work tool.

All even functions go through the origin.

True or false: If the statement is true, explain why it must be true using the definitions of even and odd functions. If it is false, provide a counterexample in the Show Your Work tool.

If each term in a polynomial function has an even exponent, the function is even.