Which statement correctly describes the relationship between a polynomial's degree and its symmetry?

A polynomial with an even degree is always an even function.

A polynomial with an odd degree is always an odd function.

A polynomial's degree does not determine its symmetry.

A polynomial must have a constant term to be an even function.

Transformations of Polynomial Functions Practice — Grade 11 math

Lesson 7: Transformations of Polynomial Functions — Practice Questions

1. Which statement correctly describes the relationship between a polynomial's degree and its symmetry?
- A. A polynomial with an even degree is always an even function.
- B. A polynomial with an odd degree is always an odd function.
- C. A polynomial's degree does not determine its symmetry.
- D. A polynomial must have a constant term to be an even function.
2. Determine if the function $g(x) = x^6 + 2x^3$ is even, odd, or neither.
- A. Even
- B. Odd
- C. Neither
- D. Both even and odd
3. Consider the function $h(x) = x^5 - 4$. What type of symmetry does this function have?
- A. Even
- B. Odd
- C. Neither
- D. Symmetric about the x-axis
4. The function $f(x) = x^7 - 2x^3 + c$ is an odd function only if the constant $c$ is equal to ___.
5. The polynomial $p(x) = 2x^4 - 3x^2 + 7$ has a degree of 4. What is the symmetry of this function?
- A. Odd
- B. Even
- C. Neither
- D. Cannot be determined
6. How is the graph of $g(x) = -(x - 5)^3 + 2$ transformed from the parent function $f(x) = x^3$?
- A. Reflected over the x-axis, shifted 5 units left, and 2 units down.
- B. Reflected over the x-axis, shifted 5 units right, and 2 units up.
- C. Shifted 5 units right and 2 units up.
- D. Reflected over the y-axis, shifted 5 units right, and 2 units up.
7. A transformation of $f(x) = x^4$ is shifted 3 units left, 7 units down, and vertically stretched by a factor of 2. If the new function is $g(x)$, then $g(x) = \_\_\_$.
8. The graph of $f(x) = x^3$ is translated 4 units to the right and 9 units up. What is the value of $h$ in the transformed function $g(x) = a(x - h)^3 + k$?
- A. 4
- B. -4
- C. 9
- D. -9
9. The function $p(x) = \frac{1}{2}(x+1)^4 - 6$ is a transformation of $f(x) = x^4$. The vertical shift is ___ units down.
10. How does the graph of $g(x) = -4(x+1)^3$ compare to the graph of the parent function $f(x) = x^3$?
- A. It is reflected over the x-axis and vertically stretched by a factor of 4.
- B. It is reflected over the x-axis and vertically compressed by a factor of 4.
- C. It is reflected over the y-axis and vertically stretched by a factor of 4.
- D. It is only vertically stretched by a factor of 4.