Relations and Functions
In an ordered pair, which number represents the input? the output?
Input = first number
Output = second number
Write a function rule for the statement.
The output is half of the input.
y = 1/2 * x
p.261 #5
y = (4/3)x + 2
p.270 #7
p.276 #7
The volume of the balloon increases at a constant rate, then stays constant, then increases at a constant rate, then stays constant, and then increases at a constant rate.
p.246 #7
(1,8)
(3,8)
(3,4)
(5,6)
(7,2)
Write a function rule for the statement.
The output is one more than twice the input.
y = 2x + 1
p.261 #8
y = 2x
p.270 #8
Nonlinear - graph does not increase at a constant rate of change.
p.276 #12
The loan balance remains constant, then decreases instantly, then remains constant, then decreases instantly, then remains constant.
p.246 #9
No
Find the value of y for the given value of x.
y = 1 - 2x
x = 9
-17
Explain why the vertical line does not represent a linear function.
The vertical line has more than one output for its input. ie. x=3
p.270 #9
Linear - as x increase by 6, y increases by 4.
p.276 #13
a) The usage decreases at an increasing rate.
b) The usage decreases at a decreasing rate.
p.246 #12
In order for a relation to be a function, each input must be paired with exactly one output. So, the relation is not a function.
Find the value of y for the given value of x.
y = x/2 + 9
x = -12
3
p.261 #11b&d
b) y = 3x
d) $9
p.271 #12
Linear - you can rewrite the equation in slope intercept form.
p.277 #15
See graph.
p.247 #13
Input --> Output
-3 ---> -3
-1 ---> -1
1 ---> 1
3 ---> 3
As each input increases by 2, the output increases by 2.
Graph the function.
y = -5x + 3
y-intercept at 3
slope of -5
p.262 #15
a) hiking
b) 22.5 calories
p.271 #17
a) Nonlinear - does not increase at a constant rate of change.
b) Tree B - Tree A is at 15 feet in 10 years and Tree B is already at 23 feet after 9 years.
p.277 #19a&b
a) The supply curve increases at an increasing rate so suppliers produce more and more as price increases. The demand curve decreases at a decreasing rate so consumers buy less and less as price increases.
b) Surplus means more than is needed. Shortage means less than is needed.