![]() In this case, the equation yielded two solutions: x = 0 and x = 3. Set the third expression equal to zero, and solve. Set the second expression equal to zero, and solve.Įven though the equation can be solved, x = 8 is not in second section of the domain therefore, there are no x -intercepts in the second section section of the domain. Since five cannot equal 0, there are no x -intercepts in the first section of the domain. Set the first expression equal to zero, and solve. ![]() After solving for x, make sure that the solution(s) of each equation exist in the corresponding domain. To solve the equation f(x) = 0, set each expression in the piecewise function equal to zero. To find the x -intercept, or zero, of the piecewise function, let f(x) = 0. Example 2:įind the x - and y -intercepts of the following piecewise function. When the graph of a function touches or crosses the y -axis, x = 0. The y -intercepts of a function are the points where the graph of the function touches or crosses the y -axis. When the graph of a function touches or crosses the x -axis, f(x) = 0. ![]() The x -intercepts, or zeros, of a function are the points where the graph of the function touches or crosses the x -axis. Therefore, the domain of the function is. There is an open circle at x = 3, which indicates that the value is not in the domain of the function. There is a closed circle at x = -7, which indicates that the value is in the domain of the function. ![]() These discontinuities do not affect the domain of this function because the piecewise function is still defined at each discontinuity. It is seen that the graph has breaks, known as discontinuities, at x = -3 and x = 1. The given function is a piecewise function, and the domain of a piecewise function is the set of all possible x -values. What is the domain of the function graphed below? Solution: The range of a function is the set of all possible real output values, usually represented by y. The domain of a function is the set of all possible real input values, usually represented by x. Isn't defined at x equals 9.A piecewise function is a function defined by two or more expressions, where each expression is associated with a unique interval of the function's domain. Where we have a filled-in circle for x equals 9 so the function g actually So that means that while it's not, you can't say that theįunction is -3 right over there and there's no other place Point right over here, we have an open circle. You might be tempted to say it's -3, but you see, at this So g(9), that's when x is 9 and we go down here. So 4.0000, as many, just slightly above 4, the value of our function But as soon as we getĪny amount larger than 4, then the function drops down to this. Is circled in up here and it's hollow down here. How did I know that? Well I know that g(4) is 7 and not -3 because we have this dot So g(4) is still 7, but as soon as we go above 4, we drop down over here, so g(4.00001) is going to be -3. g(3.99999) 3.99999, almost 4, so let's draw a dotted line right here, it's gonna be almost 4, well g(3.99999) is going to be 7. So this is going to beĮqual to 3 right over here. So g(-3.0001), so -3.0001, so that's right over here and g of that, we see is equal to 3. It starts when x equals -9, it's at 3, and then it jumps up, and then it jumps down. Below is a graph of the step function g(x) so we can see g(x) right over here. Because we're using this case, you could almost ignore h(-3) is going to be -3 to the third power which is -27. So we're going to use the first case again and so for h(-3), we're gonna take -3 to the third power. If it was positive 30, we would use this case. If it was positive three, we would use this case. Negative infinity and zero, so we're gonna use thisĬase right over here. What is the value of h(-3)? See when h is -3, which case do we use? We use this case if our x f(10) is 150, 'cause we used this case up here, 'cause t is -10. 10 squared, that's positive 100 and then negative, or subtracting 5 times -10, this is going to be subtracting -50 or you're going to add 50, so this is going to be equal to 150. 10 squared minus 5 times, actually I don't have a denominator there, I don't know why I wrote it so high. So f(-10) is going to be equal to -10, everywhere we see a t here, we substitute it with a -10. So we wanna use this case right over here. If t is less than or equal to -10, we use this top case, right over here and t is equal to -10, that's the one that And then they ask us what is the value of f(-10)? So t is going to be equal to -10, so which case do we use? So let's see. And if t is greater than or equal to -2, we use this case. If t is between -10 and -2, we use this case. Following piecewise function and we say f(t) is equal to and they tell us what it's equal to based on what t is, so if t is less than or equal to -10, we use this case.
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