# Algebra

A student claims that the function f(x)=x^4 + kx^2 + 1 is an even function. Which statement best describes the student's claim?

The student's claim is true for all values of k.
The student's claim is only true for even values of k.
The student's claim is not true for any value of k.
The student's claim is only true for odd values of k.

I think the answer is the third one or fourth one but I am not sure because I substituted "x" with 1 and -1 into the equation and got the answers:
(1)= 2k
(-1)= k

1. 👍 0
2. 👎 0
3. 👁 521
1. A function is even if f(a) = f(-a)

let's test it

f(a) = a^4 + ka^2 + 1
f(-a) = (-a)^4 + k(-a)^2 + 1 = a^4 + ka^2 + 1

so, what do you think?

1. 👍 0
2. 👎 0
2. That they are correct, this is an even function ?

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Calculus. I need help!

Write the composite function in the form f(g(x)). [Identify the inner function u=g(x) and the outer function y=f(u).] Then find the derivative dy/dx. y=√sinx √ is square root.

asked by danny on February 25, 2012
2. ### English Language

Grammatical Name and Function of "What they were planning is very good." Grammatical Name and Function of "The news that Ngozi has recovered is true." Grammatical Name and Function of "He stopped shouting only when he got into the

asked by Sannu Xeno on September 12, 2019
3. ### Algebra 2 check my last answer?!

A cosine function has a period of 3, a maximum value of 20, and a minimum value of 0. The function is a reflection of its parent function over the x-axis. Which function could be the function described? f(x)=10cos(3x)−10

asked by Nelly on May 4, 2017
4. ### software

The questions ask List four major functions of an OS. My answer: Function 1: Provide a user interface Function 2: Manage files Function 3: Manage hardware Function 4: Manage applications Is my answer correct?

asked by DJ on February 12, 2013
1. ### Math

compare the parent function f(x)=x^2 to the quadractic function f(x)=-2x^2-6. the 6 in the function does which of the following? a.it makes the graph narrower than the parent function. b.it makes the graph wider than the parent

2. ### Algebra 2

The graph of an absolute value function opens up and has a vertex of (0, -3). The domain of the function is . The range of the function is

asked by Taylor on January 18, 2020
3. ### Algebra (math)

The graph represents function 1 and the equation represents function 2: A graph with numbers 0 to 4 on the x-axis and y-axis at increments of 1. A horizontal straight line is drawn joining the ordered pairs 0, 3 and 4, 3. Function

asked by Winchester on January 4, 2017
4. ### Math I need help ASAP!

1) Identify the function rule shown in the table. Function Table n - 3, 4, 5, 6 y - 2, 1, 0, -1 a. y = 2 + n b. y = 5n c. y = 5 - n d. not enough information ** 2) What is the values of the function y = -2x - 4 for x = 0,1,2 and

asked by Talea on April 7, 2015
1. ### Math

Which combination could create the function f(x)= x√x? adding a rational function and a linear function adding a linear function and a logarithmic function multiplying a linear function and a square-root function dividing an

asked by tobeymaguire on June 19, 2020
2. ### Math

The graph represents function 1 and the equation represents function 2: A graph with numbers 0 to 4 on the x-axis and y-axis at increments of 1. A horizontal straight line is drawn joining the ordered pairs 0, 3 and 4, 3. Function

asked by Marc-Anthony on January 11, 2016
3. ### Math

Assume it costs Microsoft \$4,300 to manufacture 7 Xbox 360s and \$8,290 to manufacture 14. Obtain the corresponding linear cost function. C(x)= (what formula do I use to get the cost function, because I can't get it) What was the

asked by Amie on February 19, 2012
4. ### Calculus (Continuity)

If the following function is continuous, what is the value of a + b? f(x) = {3x^2 - 2x +1, if x < 0 a cos(x) + b, if 0

asked by Mishaka on October 22, 2011