GRE Math Slides 60-82

Pataasin ang iyong marka sa homework at exams ngayon gamit ang Quizwiz!

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?


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