Consider the piecewise-defined function given by the graph. what are these values? a) f(–3) = b) f(–1) = c) f(3) =

Answers:

f(-3) = -1

f(-1) = 2

f(3) = 5

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Explanations:

Draw a vertical line through -3 on the x axis. Make sure this vertical line crosses the orange graph. Mark this point of intersection and then draw a horizontal line from this point to the y axis. You should find that it touches -1 on the y axis. Check out the attached image to see this process in action.

Those steps basically say that x = -3 leads to y = -1. Since y = f(x), this means f(-3) = -1

Through similar steps, you should find that f(-1) = 2 and f(3) = 5

Note that the open hole/circle does not count. So if you land on an open hole, just keep going until you hit a closed circle on the other piece of the graph.

A) f (–3) = -1

B) f (–1) = 2

C) f (3) = 5

Straight-line equations are mathematical equations that are described in the plane of cartesian coordinates

General formula

or

y = mx + c

Where

m = straight-line gradient which is the slope of the line

x1, y1 = the Cartesian coordinate that is crossed by the line

c = constant

The formula for a gradient (m) between 2 points in a line

m = Δy / Δx

or we can use:

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

We look for 3 pieces of function from the graph

1. graph 1 is a straight line that passes through 2 points : (-4.0) and (-1, -3) so that the straight line equation:

2. graph 2 is a straight line with the equation: \

3. graph 1 is a straight line that passes through 2 points,  (3.5) and (5.1) so that the straight line equation  :

A function made up of 3 pieces:

a solid dot means "including",

an open dot means "not including"

A) f (–3) =

Because -3 <-1, the function used is y = -x-4, so

f (-3) = - (- 3) -4

f (-3) = 3-4

f (-3) = -1

B) f (–1) =

Because x = -1, the function used y = 2, so

f (-1) = 2

C) f (3) =

Because x = 3, the function used is = -2x + 11, so

f (3) = -2 (3) +11

f (3) = -6 + 11

f (3) = 5

Piecewise Functions

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the inverse of the function

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domain of the function

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