Precalc. 1.1

Shape of an y=1/x graph.

2 separate graphs - 1 in Q1 & 1 in Q4 curved like a C No Origin - HA @ x=0 & VA @ y=0

T or F : Since the graph does not intersect the​ y-axis at any​ point, there is no​ y-intercept.

True

Shape of an y=(-x^2) graph

U facing downwards Origin @ (0,0) - (-2,-4) (2,-4)

Shape of an y=x^2 graph

U facing upwards because it is positive Origin @ (0,0) - (2,4) (-2,4)

Shape of an y=lxl (absolute value) graph

V facing upwards Origin @ (0,0) - (1,1) (2,2)

What is an x-intercept? Y-intercept?

X-intercept: Point where the graph intersects the x-axis. (x-coordinate of that point) Y-intercept : Point where the graph intersects the y-axis. (y-coordinate of that point)

In the rectangular coordinate​ system, the point of intersection of the horizontal axis and the vertical axis is called the _________.

origin

The axes of the rectangular coordinate system divide the plane into regions called​ _______. There are​ _______ of these regions.

quadrants / 4

The ordered pair​ (4,19) is​ a/an _______ of the equation y=x^2+3 because when 4 is substituted for x and 19 is substituted for​ y, the result is a true statement.​ Thus, it can be said that​ (4,19) _______ the equation.

solution / satisfies

In the rectangular coordinate​ system, the horizontal number line is called the _______.

x-axis

The first number in an ordered pair such as ​(2​,8​) is called the ________. The second number in such an ordered pair is called the ____________.

x-coordinate / y-coordinate

The​ x-coordinate of a point where a graph crosses the​ x-axis is called​ a/an _______. The​ y-coordinate of such a point is always​ _______.

x-intercept / 0

In the rectangular coordinate​ system, the vertical number line is called the​ _______.

y-axis

The​ y-coordinate of a point where a graph crosses the​ y-axis is called​ a/an _______. The​ x-coordinate of such a point is always​ _______.

y-intercept / 0

Express Mathematically : The​ y-value is five more than four times the​ x-value.

y=4x+5

The​ y-value is four increased by the square of the x​-value.

y=x^2+4

How do you know if the formula overestimates or underestimates the graph?

Compare the data, if the formulas number is higher the formula overestimates the graph's data.

Shape of an y=x^3 graph

Curve constantly increasing Origin @ (0,0) - (1,1) (-1,-1) (2, 9) (-2,-9)

How do you find an x-intercept? Y-intercept?

Scan the x-axis (horizontal) until you find a point that the line of the graph passes through. Ex: 3. Scan the y-axis (vertical) until you find a point that the line of the graph passes through. Ex: -2