Functions
What is a function?
A relation where each input has exactly one output.
What is the slope-intercept form of a linear equation?
y=mx+b where mm is the slope and bb is the y-intercept.
What is the general form of an exponential function?
f(x)=abx where aa is the initial value and bb is the growth factor.
What is the shape of the graph of a quadratic function called?
Parabola
How do you find the roots of the equation x2−5x+6=0
Factor to (x−2)(x−3)=0, so roots are x=2 and x=3
What is the domain of a function?
The set of all possible input values (x-values).
How do you calculate the slope between two points (x1,y1) and (x2,y2)?
m= (y2-y1) / (x2-x1)
What does the base of an exponential function indicate?
The rate at which the function is growing or decaying.
If the leading coefficient of a quadratic function is negative, which way does the parabola open?
Downward
What is the standard form of a quadratic equation?
ax2 + bx + c = 0
How can you tell if a relation is a function from its graph?
Use the vertical line test; if a vertical line crosses the graph at more than one point, it's not a function.
What does it mean if two linear functions have the same slope?
They are parallel lines and will never intersect.
How do you determine the y-intercept of an exponential function?
The y-intercept is the value of f(0)
How can you determine if a quadratic function has a maximum or minimum value?
The vertex's y-coordinate determines it; if it opens upwards, it has a minimum; if downwards, a maximum.
Use the quadratic formula to solve for xx in the equation 2x2+4x−6=0
x=1 and x=-3
What does it mean for two functions to be inverse functions?
They "undo" each other; if f(g(x))=x and g(f(x))=x.
How can you graph a linear function using the slope and y-intercept?
Start at the y-intercept and use the slope to find another point.
What is the difference between exponential growth and linear growth?
Exponential growth increases at a rate proportional to its current value, while linear growth increases by a constant amount.
What is the axis of symmetry for the quadratic function y=x2−6x+8?
x=3
How can you determine if the roots of a quadratic equation are rational or irrational using the quadratic formula?
If the discriminant b2−4ac is a perfect square, the roots are rational; if it is not a perfect square, the roots are irrational.
How do you determine if a function is increasing or decreasing?
A function is increasing if the output increases as the input increases, and decreasing if the output decreases as the input increases.
What is the point of intersection of the lines represented by the equations: y=2x+3 and y=−x+1?
(2/3, 7/3)
Solve for x in the equation 3x=81.
x=4
81=34
How can you determine the width of a parabola represented by the quadratic function y=ax2+bx+c?
The absolute value of aa affects the width; larger absolute values narrow the parabola, while smaller absolute values widen it.
Solve the equation 2x2−8=0 for x
x=2 and x=5