GRE Math Slides 60-82
V-shaped, y = x and y = -x
A piecewise-defined function creates a graph that is _____ shaped and consists of two linear pieces _____ and _____ joined at the origin.
(x − 6)² + (y + 5)² = 9
A circle has center (6, -5) and radius 3. What is its equation?
x² + y² = 100
A circle is centered on the origin and has a radius of 10. What is its equation?
the least interest rate is approximately 4.9 percent per year, compounded quarterly (Pg. 60-61)
A college student expects to earn at least $1,000 in interest on an initial investment of $20,000. If the money is invested for one year at an annual interest rate of r percent, compounded quarterly, what is the least annual interest rate that would achieve the goal? (Give your answer to the nearest 0.1 percent.)
0
A horizontal line has a slope of ____.
symmetric with itself about the vertical line that passes through its vertex
Every parabola that is the graph of a quadratic equation of the form y = ax^2 + bx + c is ________.
7.5
Find the distance between the two points Q(-2, -3) and R (4, 1.5). (Use diagram on page 64).
(4, -1) (Pg. 67)
Find the point where these 2 linear equations meet. 4x + 3y = 13 x + 2y = 2
y = 0.75x - 1.5
Give the equation of line QR: Q(-2,-3), R (4, 1.5). The diagram for it is on page 66.
y = 1/2x - 5/2
Given the line y = 2x + 5, find the reflection of this.
I, II III, IV : going counter clockwise starting from the top right
How are the 4 quadrants noted?
To graph a function in the xy-plane, you represent each input x and its corresponding output f (x) as a point (x, y), where y = f (x). In other words, you use the x-axis for the input and the y-axis for the output.
How do you graph a function on a coordinate plane?
$10,300 (Pg. 59)
If $10,000 is invested at a simple annual interest rate of 6 percent, what is the value of the investment after half a year?
it opens downward and the vertex is its highest point
If a is negative, what happens to the parabola?
it opens upward and the vertex is its lowest point
If a is positive, what happens to the parabola?
$902 should be invested (Pg. 59- 60)
If an amount P is to be invested at an annual interest rate of 3.5 percent, compounded annually, what should be the value of P so that the value of the investment is $1,000 at the end of 3 years? (Give your answer to the nearest dollar.)
y = x²
If there is a function defined by g(x) = x², what would the graph be?
if their slopes are negative reciprocals of each other
If two lines are perpendicular, what will their slopes be?
y ≤ Means that it is equal to that line but also all the points below the line and vise versa for ≥
If you are given a set of inequalities to plot on a graph, what do they mean?
Pythagorean theorem
The distance between two points in the xy-plane can be found by using the ______.
y = b (b is the y intercept)
The equation of every horizontal line is ______.
x = a (a is the x intercept)
The equation of every vertical line has the form:
straight line on the xy-plane
The graph of a linear equation of the form y = mx b i+s a _______.
parabola
The graph of a quadratic equation of the form y = ax^2 +bx +c, where a, b, and c are constants and a ≠ 0, is a ________.
a circle with its centre at the point (a,b) and with radius r > 0.
The graph of an equation of the form (x − a)^2 + (y − b)^2 = r^2 is _______.
shrunk vertically by a factor of c if 0 < c < 1.
The graph of ch(x) is the graph of h(x) shrunk _____.
stretched vertically by a factor of c if c > 1
The graph of ch(x) is the graph of h(x) stretched _____.
shifted to the right by 1 unit and then stretched vertically by a factor of 2
The graph of f (x) = 2 | x - 1 | is the graph of y = | x | ____
by a factor of 1/4 and then reflected in the x-axis
The graph of g(x) = - x²/4 is the graph of y = x² ______.
shifted to the left by c units
The graph of h(x + c) is the graph of h(x) _______.
shifted to the right by c units
The graph of h(x − c) is the graph of h(x) ______.
shifted upward by c units
The graph of h(x) + c is the graph of h(x) ______.
shifted to the right by 1 unit and then shrunk, or contracted, vertically toward the x-axis by a factor of 1/2
The graph of h(x) = 1/2 | x - 1 | is the graph of y = | x| shifted _____
shifted downward by c units
The graph of h(x) − c is the graph of h(x) ______.
origin, denoted by the O
The point where the two axes intersect is called the _____.
y2 - y1 _______ x2 - x1
The slope of a line passing through 2 points is defined as:
the solutions of the equation ax^2 + bx + c = 0 (the quadratic equation)
The x intercepts of a parabola are ______.
parallel
Two lines are _____ if they have equal slopes.
rectangular coordinate system, often called the xy-coordinate system or xy-plane
Two real number lines that are perpendicular to each other and that intersect at their respective zero points define a _____ aka a _____ aka a ______.
If you have two lines that are reflections of each other, it is the one in the middle of the two.
What does a line of symmetry?
half of a parabola
What does the graph of y = √x or y = -√x look like?
If x = 0, the point lies on the y axis. If y = 0, the point lies on the x axis.
What happens if x = 0 or if y = 0?
it is expressed as a piecewise-defined function: { x, x ≥ 0 h(x) = { -x, x < 0
What happens when you are trying to graph h(x) = |x|
it is the set of all points whose ordered pairs (x, y) satisfy the equation.
What is the graph of an equation?
It is the graph y = |x| shifted upward by 2 units
What is the graph of f(x) = |x| + 2 ?
It is the graph of y = x² shifted to the left by 1 unit.
What is the graph of g(x) = (x 1)² ?
It is the graph of y = x² shifted to the right by 4 units
What is the graph of j(x) = (x 4)² ?
The graph of k(x) = |x| shifted downward by 5 units
What is the graph of k(x) = |x| -5 ?
It passes through the origin and has a slope of 1. It is diagonal across the whole thing.
What is the line y = x?
m is the slope, b is the y intercept
What is the slope and what is the y intercept of the equation y = mx + b?
the y coordinates of the points at which the graph intersects the y axis
What is the y intercept?
-1/2x
What would the slope be of a line perpendicular to this one: y = 2x + 5?
the point at which the two graphs intersect
When you are given 2 equations, what is the solution to them?