The graph of f(x) = 2x + 3 shifts 10 units to the right when it is replaced with the graph of f(x) = 2x − k. what is the value of k?

ANSWER

EXPLANATION

The given function is

The translation that shifts this function 10 units to the right is

This implies that

We expand the parenthesis to get:

Comparing this equation with

we have

k=17

The new function would be f(x)=2x-17

In the previous function when u put x=0 you got 3.

Now when the function moves 10 units to the right you still have to get y=3 for x=10. So

2x-k=3 substitute 10 for x

20-k=3 solve for k

K=17.

third choice down

step-by-step explanation:

the first inequality is based on the number of adults and campers, and the second inequality is based on the cost of feeding both the adult and the camper.

we know that there is room for 525 people max.   it's ok to have less than 525, but it's not ok to have more than 525, so the inequality is less than or equal to.   the number combination of adults (x) and campers (y) cannot exceed this 525 max.   therefore:

x + y ≤ 525

now we talk about cost.   it costs $9 to feed one adult, so depending upon the number of adults you have (x) depends upon how much it will cost to feed that number of adults.   same with the campers, who cost $5 to feed.   the adults can be represented by 9x and the campers can be represented by 5y.   since the budget cannot exceed 1,200, the second inequality is:

9x + 5y ≤ 1200