I’m kinda confused? Can you help me ?

Which of the following is an even function g(x) = (x – 1)2 + 1g(x) = 2x2 + 1g(x) = 4x + 2g(x) = 2x

GuDViN [60]

An even function can be reflected about the y axis and map onto itself
example: y=x^2

an odd function can be reflected about the origin and map onto itself
example: y=x^3

a simple test is the following

if f(x) is even then f(-x)=f(x)
if f(x) is odd then f(-x)=-f(x)

so

even function
subsitute -x for each and see if we get the same function
remember to fully expand these

g(x)=(x-1)^2+1=x^2-2x+1+1=x^2-2x+2 is the original one

g(x)=(x-1)^2+1
g(-x)=(-x-1)^2+1
g(-x)=(1)(x+1)^2+1
g(-x)=x^2+2x+1+1
g(-x)=x^2+2x+2
not same because the original has -2x
not even

g(x)=2x^2+1
g(-x)=2(-x)^2+1
g(-x)=2x^2+1
same, it's even

g(x)=4x+2
g(-x)=4(-x)+2
g(-x)=-4x+2
not the same, not even

g(x)=2x
g(-x)=2(-x)
g(-x)=-2x
not same, not even

g(x)=2x²+1 is the even function

8 0

3 years ago

Read 2 more answers

Graph the system of linear inequalities, please explain the process in solving this problem so I know how to do ones similar to

Ierofanga [76]

Graph the system of linear inequalities

x + y > 5

- x - y < -5

First we graph x + y >5

Step 1: replace > symbol by = sign

x + y =5

step 2 : Solve the equation for y

x + y =5 (subtract x from both sides)

y = 5 - x

step 3: Now we make a table . plug in some number for x and find out y

x -----> y

-1 -----> 6 ( y=5-x => y=5-(-1)= 6)

0 -----> 5 ( y=5-x => y=5-(0)= 5)

1 -----> 4 ( y=5-x => y=5-(1)= 4)

Step 4: we graph the table.

step 5: Shade the region that satisfies our inequality

x + y > 5. Greater than symbol implies that we shade the graph to the right

Graphing second inequality - x - y < -5

All terms have negative sign . so divide all the terms by -1. When we divide an inequality by -1 its sign changes

- x - y < -5 becomes x + y > 5

Follow the same steps to graph this inequality

After dividing the second equation by -1 , we got the same as the first equation.

So we will get the same graph

Both graphs overlaps

The graph of first and second inequality overlaps

The graph is attached below

4 0

3 years ago

By what number should I multiply 1 1/4 to obtain 3/4

aleksklad [387]

Multiply by 3/5 (three fifths)

4 0

3 years ago

A⋅a/\2⋅a/\3=?? I need help ASAP

wolverine [178]

Answer:

a^6

Step-by-step explanation:

a^1 * a^2 * a^3 = 1+2+3(add all power when same variable)

a^6

7 0

3 years ago

karen is 3 yrs younger than floyd. floyd is 2 years older than maria. marias age is the smallest two-digit number. how old are t

Alinara [238K]

Answer:

Maria is 10, Floyd is 8, and Karen is 5.

Step-by-step explanation:

Having said that Maria's age was the smallest two-digit number, that's ten. (10). If Floyd is 2 years younger then 10-2=8. Karen is 3 years younger, so she would be 8-3=5.

4 0

3 years ago