Functions
What does it mean for a relation, graph, or table to be a function?
Only one input per output.
What does the equation and the graph of a linear function look like?
y=mx+b and it makes a line
What does the equation and graph look like for an exponential function?
y=abx and it makes a curve
What does the graph and equation look like for a quadratic function?
y=ax2+bx+c and it is a parabola
Solve:
(x+3)(x+4)
x2+7x+12
What is domain and range?
Domain are the x values and range are the y values.
What does the m and b stand for in slope intercept form?
m is the slope and b is the y-intercept
What three things are needed in order to solve an exponential word problem?
a (inital value), r (rate), and t (time)
Where can I find the vertex of a quadratic function?
the highest or lowest point of the graph
Solve:
(x2+2x+5) + (4x-2)
x2+6x+3
What is the difference between an even function and an odd function?
Even functions are symmetrical about the y-axis and odd functions are symmetrical about the y-axis
What is the slope formula?
y2-y1/x2-x1
If b is greater than one this is exponential
growth
Factor the following:
x2+12x+27
(x+3)(x+9)
What is the greater than sign of an inequality?
>
What is f(2) for the function 6x - 5
7
Solve this literal equation for x? y=mx+b
x=y-b/m
What are the exponential growth and decay word problem formulas
growth: y=a(1+r)t
decay: y=a(1-r)t
What is the quadratic formula?
see board
Which variable do we use to find the correlation coefficient?
r
Solve this for r:
V=r2h
see board
A manager of a self-service car wash charges a flat fee in addition to a fee per minute, x, for use of the services. The expression 5 + 0.75x models the scenario. What is true about the slope and y-intercept?
$5 is the flat rate and 0.75 is the service charge
The value of a car t years after being purchased can be modeled by the function V(t) = 16,000(0.85). What does the 0.85 represent in the function?
The value of the car decreases by 15% each year
Find the following function's vertex, aos, domain, and range.
y=x2-10x+40
(5,15), x=5, all real numbers, y≥15
When solving systems of equations, where do I find my solution?
where the two points intersect