If you're seeing this message, it means we're having trouble loading external resources on our website. Show If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. The y-intercept of a function is the point at which the graph of the function crosses the y-axis. Although a function can have many x-intercepts, a function can only have one y-intercept. This is because a function must pass the vertical line test in order for it to be a function; if a vertical line intersects the graph of a relation at more than one point, it is not a function. Example The relation in the following figure is a function because it passes the vertical line test. The relation in the following figure is not a function because it fails the vertical line test. It has more than one y-intercept and many points at which a vertical line would cross the graph more than once. How to find the y-intercept of a functionTo find the y-intercept of a function, we need to find the point on the graph where x = 0. Given a function, f(x), the y-intercept occurs at f(0). In general, what is the y intercept of the function # F(x) = a * b^x# ?Algebra 1 AnswerCesareo R. Jul 5, 2016 #F(0)=a# Explanation:The#y#intercept is when#x = 0#then #F(0) = a cdot b^0 = a# Answer link Related questions
Impact of this question3627 views around the world You can reuse this answer In order to get the y-intercept, just plug in 0 as the x-value then you should get#0^3-3(0)-4(0)#or in other words, 0. X-Intercept Now here's where things start to get more complicated. Firstly, we should determine how many zeroes there are. We can see that from the x^3, there are 3 roots (because the power on the leading coefficient determines the amount of roots). Then, we can see that all of the numbers in the equation have a x in common. We should take out that x in all the numbers in order to get#x(x^2-3x-4). # Lastly, we expand the function in the middle with#x(x-4)(x+1).# If we plug in 4, 4 would cancel out with x-4 to equal 0, and the whole equation would be multiplied by 0 to equal zero, therefore another 0 is 4,0. Lastly, if we plug in -1, it would cancel with#x+1#to equal 0, which again would multiply the whole equation by 0 in order to equal 0. Therefore, the last zero is -1,0. A linear function is a process that permits the description of the straight line on the coordinate plane. For example, y = 2x – 1 designates the straight line on the coordinate plane, and therefore it conveys a linear process. As y can be substituted by f(x), this process can be registered as f(x) = 2x – 1. It is one of the state f(x) = mx + b , here ‘m’ and ‘b’ denotes the real numbers. It’s examining like the slope-intercept shape of a bar which is provided by y = mx + b because the linear process denotes a bar i.e. it’s a graph line. Here, ‘m’ is the pitch of the string ‘b’ is the y-intercept of the bar ‘x’ is the separate variable ‘y’ (or f(x)) is the conditional variable A linear procedure is also known as an algebraic procedure. Example of linear functions
The linear function formula is used to represent the objective function of the linear programming problems, which helps to maximize profits. Linear function FormulaThe data is provided as a graph about a process, it is linear if the graph is a bar. If the data is provided in the state of algebraic structure about the function, then it is linear if it is of the form f(x) = mx+b. But to see whether the shared data in a table form describe a linear equation or not we have to, • Calculate the distinctions in y-values • Calculate the distinctions in the x-axis • Check whether the balance of the dissimilarity in y-values to the dissimilarity in x-values is always steady. Graphing of a linear function As we comprehend to plot a line on a graph we require any two points on it. If we discover two points we only have to devise them on the graph merge them by a line and spread from both flanks. The graph of a linear function f(x) = mx + b is
Graphing a linear function by finding two points To discover two pinpoints on a linear function (line) f(x)=mx+b, consider some unexpected values for ‘x’ and have to replace these values to find the connected values of y. This method is presented by an instance where we are proceeding to graph the function f(x) = 2x + 4.
Graphing of linear function using slope and y-intercept
Domain and range of linear function The domain of the linear function is the collection of all real numbers, and actually, the scope of a linear function is also the collection of all-natural numerals figures show f(x) = 2x + 3 and g(x) = 4 −x devised on the same axes. Note: both the roles taken on the absolute value for all the values of x, mean that the part of each function is the collection of all-natural numerals (R). Examine along the x-axis to ensure. For every value of x, we have a moment on the graph. Even, the result for each of the procedures varies from negative to positive infinity, which represents the scope of either function is also R. That can be verified by examining along the y-axis, which apparently delivers that there is a moment on each graph for every y-value. Thus, when the slope m ≠ 0, •The parts of a linear function = R •The scope of a linear function = R
The inverse of a linear function Inverse of the linear function f(x) = ax + b is shown by a function f-1(x) such that f(f-1(x)) = f-1(f(x)) = x. The method of seeing the inverse of a linear function is presented through an instance where we are heading to find the inverse of a function f(x) = 2x + 4.
Piecewise linear function Periodically the linear function may not be described uniformly via its habitat. It may be described in two better routes as its habitat separates in two or more methods. In these changes, it is understood as a piecewise linear function. Let’s take a sample. Sample ProblemsQuestion 1: Find the linear function that has two points (-2, 17) and (1, 26) on it. Solution:
Question 2: Decide whether the subsequent data from the subsequent table describes a linear function. XY35552373111471355Solution:
Question 3: Plot graph y = 3x + 2 is a linear equation Solution:
Question 4: Plot the graph of the following equation 3x + 2y − 4 = 0 Solution:
Question 5: Plot the graph of the following piecewise linear function.
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