Find a formula for a function f(x) for which f(-2) = 3.

Expert Answers
hala718 eNotes educator| Certified Educator

It depends on the degree of the function:

for the linear function for example:

f(x) = ax+b

f(-2) = -2a + b = 3

==> b = 3+2a

Let a = 1  ==> b = 3+2*1 = 5

==> f(x) = x + 5 

Let a= 2  ==> b = 2*2 + 3 = 7

==> f(x) = 2x + 7

atyourservice | Student

f(-2) = 3

f(-2) means that you plug in -2 for x in order to get 3.

A fast way of doing it is by just adding 2 to 3 and seeing what you get (5) and then you use that number plus x

so an equation that would work would be:

f(-2) = x + 5

Wiggin42 | Student

Find a formula for a function f(x) for which f(-2) = 3.

Since we are given no other conditions, you have quite some freedom and ease with this. 

x = -2 and y = 3

What can be done to x to make it equal y?

Adding five is an option so: 

f(x) = x + 5

Multiplying x by -3/2 is also an option so: 

f(x) = (-3/2)x 

cherryty2100 | Student

A possible answer to this question is:

f(x) = x + 5.

When you add 5 to -2 you get 3, so it works.  There are other equations that would give you f(-2) = 3, but this is probably the simplest equation.