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

Mathematics

1 answer:

lesya692 [45]3 years ago

5 0

Answer:

You may be asked to "determine algebraically" whether a function is even or odd. To do this, you take the function and plug –x in for x, and then simplify. If you end up with the exact same function that you started with (that is, if f (–x) = f (x), so all of the signs are the same), then the function is even.

Step-by-step explanation:

You might be interested in

Let g be the function given by g(x)=x^2*e^(kx) , where k is a constant. For what value of k does g have a critical point at x=2/

ArbitrLikvidat [17]

G `( x ) = $2x * e^{kx} + k x^{2} *e^{kx} = \\ = xe^{kx}(2 + kx )$
2 + k x = 0
k x = -2
k = -2: x = - 2 : 2/3 = - 2 * 3/2
k = - 3
Answer: for k= - 3, the function g ( x ) have a critical point at x = 2/3.

8 0

3 years ago

the height of a kicked soccer ball is represented by the function f(x)=8x-2x^2 where x is the number of seconds since the ball w

____ [38]

Answer:

Result at time x = 4 seconds the soccer ball hit the ground.

Step-by-step explanation:

At the moment just before the ball is kicked, it is on the ground and so the height f(x) is zero meters. After the kick, the ball goes through the air and it's path can be described by a (mountain) parabola.

So lets see after how many second (x) the height = 0 once again.

f(x) = 8x-2x^2

f(x) = 0

8x - 2x^2 = 0

Try to write the formula in two terms

-2x * (x - 4) = 0

When a product of two or more terms equals zero, then at least one of the terms must be zero.

Now solve each term = 0 separately, meaning, solve as many equations as there are terms in the product.

Any solution of term = 0 solves product = 0.

Solve the first term:

-2x = 0

Multiply left an right from the = singn with the factor -1 gives this outcome: