Consider the following piecewise-defined function. f(x){x^2 -5, x< 3
{2x+5, x> 3
find f(-4)

Results from f (-4) = 11

Set A to set B is said to be a function if each member of set A pairs is exactly one member of set B

So, one value of x is only assigned to one value of y, or one input for one output

A function can be expressed in the form of a diagram, the set of ordered pairs, or arrow diagrams

If y is a function of x, then y = f (x)

where x is the independent variable and y is the dependent variable

x is the domain and y is the result area or range

There are several forms of function including:

• 1. linear function

• 2. quadratic function

• 3. trigonometric functions

• 4. polynomial function

• 5. fraction function etc.

A function can be write as ordered pair

Ordered pairs because we write the input first, and then the output

Can be described in form

(input, output)

or

(x, f (x))

For example a set of ordered pairs

(2,4), (3,5), (4,6)

input values (as domain) 2,3,4

output values (as range) 4,5,6.

Piecewise Functions: functions that have different equations based on the input (x) value

A function made up of 2 pieces:

if we look for f (-4), then:

Because -4 is <3, so we use f (x) = x²-5, so

F (x) = x2 + 1 g (x) = 5 - x

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the inverse of the function f (x) = 2x-10

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domain of the function

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step-by-step explanation:

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.