Obtaining Equations from Piecewise Function Graphs You may be asked to write a piecewise function, given a graph. To review how to obtain equations from linear graphs, see Obtaining the Equations of a Line, and from quadratics, see Finding a Quadratic Equation from Points or a Graph.
Compound inequalities Video transcript Let's do some compound inequality problems, and these are just inequality problems that have more than one set of constraints. You're going to see what I'm talking about in a second. So the first problem I have is negative 5 is less than or equal to x minus 4, which is also less than or equal to So we have two sets of constraints on the set of x's that satisfy these equations.
So we could rewrite this compound inequality as negative 5 has to be less than or equal to x minus 4, and x minus 4 needs to be less than or equal to And then we could solve each of these separately, and then we have to remember this "and" there to think about the solution set because it has to be things that satisfy this equation and this equation.
So let's solve each of them individually. So this one over here, we can add 4 to both sides of the equation. The left-hand side, negative 5 plus 4, is negative 1. Negative 1 is less than or equal to x, right? These 4's just cancel out here and you're just left with an x on this right-hand side.
So the left, this part right here, simplifies to x needs to be greater than or equal to negative 1 or negative 1 is less than or equal to x.
So we can also write it like this. X needs to be greater than or equal to negative 1. I just swapped the sides. Now let's do this other condition here in green. Let's add 4 to both sides of this equation.
The left-hand side, we just get an x. And then the right-hand side, we get 13 plus 14, which is So we get x is less than or equal to So our two conditions, x has to be greater than or equal to negative 1 and less than or equal to So we could write this again as a compound inequality if we want.Want to write an equation to translate the graph of an absolute value equation?
This tutorial takes you through that process step-by-step!
Take an absolute value equation and perform a vertical and horizontal translation to create a new equation. Because of how absolute values behave, it is important to include negative inputs in your T-chart when graphing absolute-value functions. If you do not pick x -values that will put negatives inside the absolute value, you will usually mislead yourself as to what the graph looks like.
Specific Impulse. The specific impulse of a rocket, I sp, is the ratio of the thrust to the flow rate of the weight ejected, that is where F is thrust, q is the rate of mass flow, and g o is standard gravity ( m/s 2).. Specific impulse is expressed in seconds.
When the thrust and the flow rate remain constant throughout the burning of the propellant, the specific impulse is the time for. Learn how to solve absolute value equations and how to graph absolute value functions.
Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Oct 21, · a: determines width on parabola and absolute value functions.
h or k only affects the vertex coordinates if the function has a vertex. Otherwise, each value (that you know) on the function has to be moved left, right, up, or down based on h and k. Questions Eliciting Thinking.
Returns the cube root of a double value. For positive finite x, cbrt(-x) == -cbrt(x); that is, the cube root of a negative value is the negative of the cube root of that value's schwenkreis.coml cases: If the argument is NaN, then the result is NaN. If the argument is infinite, then the result is an infinity with the same sign as the argument. The general form of an absolute value function is f(x)=a|x-h|+k. From this form, we can draw graphs. This article reviews how to draw the graphs of absolute value functions. Questions Eliciting Thinking. Why was it necessary to use absolute value to write this equation? How many solutions do you think this equation has?
Why was it necessary to use absolute value to write this equation? How many solutions do you think this equation has?