Linear
What are the three different forms of linear equations?
Slope-intercept form: y=mx+b
Point Slope form: y - y1=m(x - x1)
Standard form: Ax + By = C
What is the equation for exponential functions?
y=abx
What is the equation for quadratic functions?
f(x) = ax2 + bx+ c
Is this linear?
3x+2y=7
Yes, it can be put into slope-intercept form.
Find the vertex, axis of symmetry, y-intercept of 2x2+4x+8.
2x2+4x+8
-4/2(2) = -4/4 = -1 aos: x=-1
2(-1)2+4(-1)+8
2(1)+4(-1)+8
2-4+8 = 6 Vertex: (-1, 6)
y-intercept: (0,8)
What is the difference between linear and nonlinear graphs?
Linear - straight line or equation is in/can be put in y=mx+b form
Nonlinear - line is not straight or the equation has an exponent of two or three or there is more than one variable being multiplied together
How is a negative power evaluated?
a-n = 1/an
A negative exponent is evaluated when it is flipped to the denominator (which was originally 1) and the exponent becomes a positive number.
What are the axis of symmetry, vertex, and y-intercept? How do you find them?
→ axis of symmetry (aos) formula: x = -b/2a - (Plug in values from function) - line of symmetry
→ vertex: maximum or minimum point - plug in axis of symmetry back into function and find y →vertex is (axis of symmetry, y)
→ y-intercept: (0,c)
Is this linear?
3xy+7x=9
No, there are two variables being multiplied by together.
What transformations are being shown?
h(x) = -1/4x2
The function is being reflected across the x-axis and is being dilated (vertical compression) by 1/4.
What is one way to graph a linear equation?
Possible Solutions
1. Table: Make a table of values and plot the coordinates or points on the graph. Choose any number of and points that you want for x to find the y. Connect the dots together to make a linear (straight) line.
2. x/y intercept: Find the x or y intercept by making the other value zero. Plot the points and connect them.
3. Slope: Plot the y-intercept (b) and use the slope (m) to plot the next point (this can be done as many times as wanted). Connect the points to form a line.
What is the domain and range for exponential functions?
Domain: All Real Numbers
Range: Can be positive real numbers, negative real numbers, y > integer, or y < integer
How do you know if the parabola opens up or down? What is the domain and range?
If a is positive → parabola opens up → minimum value (a>0)
If a is negative → parabola opens down → maximum value (a<0)
→ Domain: All Real Numbers
→ Range:
If minimum value, then y > y value of vertex
If maximum value, then y < y value of vertex
What kind of line would this inequality show on a graph and where would I shade?
y> 7x - 1
Dotted line and shade up.
How do you know what type of line to draw for inequalities?
How do you know where to shade?
< or > (dotted line)
< or > (solid line)
For > or > shade above the line.
For < or < shade below the line.
What is the graph like?
Curved.
What is the parent function for transformations?
f(x) = x2
What is the y-intercept of 6x.
6x
60
y-intercept: (0,1)
What is the best test point to use?
(0,0) --> the origin
What is a number to the 0 power?
1
What are translations, dilations, and reflections?
Translations - side/change in figure (moving up, down, left, right, or diagonal)
Vertical Translation: g(x) = x2 + k
k>0 - k units up
k<0 - |k| units down
Horizontal Translation: g(x) = (x-h)2
h>0 - h units to the right
h<0 - h units to the left
Dilation - makes graph narrower or wider
f(x) = ax2
|a| > 1 → vertical stretch
0 < |a| <1 → vertical compression
Reflection - flips across x or y axis
-f(x) → reflects across x-axis
f(-x) → reflects across y-axis