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How do you know if a graph shifts left or right?

Given a function f, a new function g ( x ) = f ( x − h ) /displaystyle g/left(x/right)=f/left(x-h/right) g(x)=f(x−h), where h is a constant, is a horizontal shift of the function f. If h is positive, the graph will shift right. If h is negative, the graph will shift left.

When adding or subtracting to a function the graph shifts?

The graph of a function can be moved up, down, left, or right by adding to or subtracting from the output or the input. Adding to the output of a function moves the graph up. Subtracting from the output of a function moves the graph down. Here are the graphs of y = f (x), y = f (x) + 2, and y = f (x) – 2.

Why does subtracting shift right?

(a+2,b) is 2 to the right from (a,b). Think of it this way, when you graph f(x-2) you need to go two steps further to the right along the x-axis to reach f(x). Therefore it shifts to the right.

What happens to the graph when you subtract a number from the function?

Informally: Adding a positive number after the x outside the parentheses shifts the graph up, adding a negative (or subtracting) shifts the graph down.

Which graph represents a function How do you know?

How To: Given a graph, use the vertical line test to determine if the graph represents a function.

  • Inspect the graph to see if any vertical line drawn would intersect the curve more than once.
  • If there is any such line, the graph does not represent a function.

What happens to the graph when a is negative?

If a is negative, the graph of the parabola opens down instead of up. The b-value of a parabola helps to determine the rate at which the parabola increases and decreases, and it also helps to determine the position of the vertex of the parabola.

What effect does a have on a graph when it is negative and between 0 and 1?

As we can see from the graphs, when 0 < |a| < 1 (|a| means absolute value of a), the parabola appears wider. When |a| > 1, the parabola appears thinner. When a is positive, the parabola opens upwards; when a is negative, the parabola opens downward.

How would you express a line with a zero slope?

The equation for a zero slope line is one where the X value may vary but the Y value will always be constant. An equation for a zero slope line will be y = b, where the line’s slope is 0 (m = 0).

What is the slope of a line that has coordinates?

The slope of a line characterizes the direction of a line. To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.

How do you find the slope of a line with two points?

There are three steps in calculating the slope of a straight line when you are not given its equation.

  1. Step One: Identify two points on the line.
  2. Step Two: Select one to be (x1, y1) and the other to be (x2, y2).
  3. Step Three: Use the slope equation to calculate slope.

What are the three equations of a line?

There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form. We review all three in this article. There are three main forms of linear equations.

What is the equation of straight line?

The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

How do you work out the equation of a line on a graph?

Equations of straight lines are in the form y = mx + c (m and c are numbers). m is the gradient of the line and c is the y-intercept (where the graph crosses the y-axis).

How do you find the equation of a line with two coordinates?

The straight line through two points will have an equation in the form y = m x + c . We can find the value of , the gradient of the line, by forming a right-angled triangle using the coordinates of the two points.

What is the Y intercept of y =- 2x?

Using the slope-intercept form, the y-intercept is 0 .