Review
Solve the literal equation for x.
1. y = 5x − 7x
2. a = 3x − 5xz
3. y = 5x − rx − 5
4. sx − tx = r
5. c = 84x − 61
6. m = 9x + x
How can you determine whether a
function is linear or nonlinear?
linear relationship - a relationship . . .
with a constant rate of
change
We can tell a relationship is linear if the table . . .
increases or decreases by the same
amount
We can tell a relationship is linear if the graph . . .
is a line
We can tell a relationship is linear if the equation . . .
can be written in the form dv = cr x iv + bp
ie: no exponents, can't divide by x or y, can't
multiply x and y together
Copy and complete each table for the sequence of similar figures. (In
parts (a) and (b), use the rectangle shown.) Graph the data in each
table. Decide whether each pattern is linear or nonlinear. Justify your
conclusion.
a. perimeters of similar rectangles
Copy and complete each table for the sequence of similar figures. (In
parts (a) and (b), use the rectangle shown.) Graph the data in each
table. Decide whether each pattern is linear or nonlinear. Justify your
conclusion.
b. areas of similar rectangles
Does the graph represent a linear or nonlinear function? Explain.
1.
2.
3.
4.
Does the table represent a linear or nonlinear function? Explain.
1.
2.
3.
4.
Linear Equations
Standard
y = 2x - 5
2x - 5y = 12
y = 4x + 9
y = 3x + 1
4
y = x - 12
5
3 x - 2y = -4
7
-3x + y = 11
5
1.
2.
3.
4.
x and y cannot be multiplied
or divided together
x and y must be in the
numerator
Pull
ax + by = c
Pull
y = mx + b
No variables have
exponents other than 1.
Pull
form
Pull
Slopeintercept
form
x and y cannot be inside
absolute value bars
Are these functions linear or non-linear?
linear
non-linear
y = -3x - 4
y = 5x3
y = 4x2 - 5
6x = 2y - 8
x+y=8
2x + 3y = 14
8 =x
y
y = |x + 4|
Does the equation represent a linear or nonlinear function?
Explain.
1. y = x + 9
2.
3.
Discrete data is counted.
Continuous data is measured.
1. The linear function y = 15.95x represents the cost y (in dollars) of x
tickets for a museum. Each customer can buy a maximum of four
tickets.
a. Find the domain of the function. Is the domain discrete or
continuous? Explain.
b. Graph the function using its domain.
2. The linear function m = 50 − 9d represents the amount m (in dollars)
of money you have after buying d DVDs. (a) Find the domain of the
function. Is the domain discrete or continuous? Explain. (b) Graph the
function using its domain.
3. A cereal bar contains 130 calories. The number c of calories
consumed is a function of the number b of bars eaten.
a. Does this situation represent a linear function? Explain.
b. Find the domain of the function. Is the domain discrete or
continuous? Explain.
c. Graph the function using its domain.
4. Is the domain discrete or continuous? Explain.
5. A 20-gallon bathtub is draining at a rate of 2.5 gallons per minute.
The number g of gallons remaining is a function of the number m of
minutes.
a. Does this situation represent a linear function? Explain.
b. Find the domain of the function. Is the domain discrete or
continuous? Explain.
c. Graph the function using its domain.
Write a real-life problem to fit the data shown in each graph. Is the
domain of each function discrete or continuous? Explain.
6.
7.
8.
9.
Find the domain and range of the function represented by the graph.
k.
l.
{x |
}
{x |
}
{y |
}
{y |
}
m.
n.
{x |
}
{y |
}
{x |
}
{y |
}
{x |
}
{y |
}
Exit Ticket: Explain how to determine when a graph has a continuous
or discrete domain.
Pg 117: 3, 4 – 14 e, 15, 16, 17 – 23 odd, 26 -­‐ 32 Which of the following equations represent linear functions? Explain.