And, you'll see the symmetry around it inĪ second. Negative, when x is negative 1, f of x is Fair enough? Then, we have this point that we have this
Y is negative 2 so that is that right overģ. When x is negative 2, this is the x axis. You have the point negative 2, negative 2. We're going to set y equal to whatever our output of I could keep going, this is in the y, and That's negative five over there on the yĪxis, y axis and then it will go to positive 7. So, let's say this is negative 1,2,3,4,5. X is equal to, this is x is equal to 0 and then this is x is equal toġ right over there and then when x is equal to, we go from negative 2Īll the way to positive. This is x is equal to negative 1, this is What the graph of the function would look And, that I think is enough points to give us a scaffold of what this graph will look When x is equal to 1, you have 3 times one So, we have, we could try, x is equal toġ. We could try, let's do one more point over
If you go one x value below the vertex, orīelow the x value of the vertex, f of x is equal to If you go one above the vertex, f of x isĮqual to negative 2. And, this is where you can see that this is the vertex, and you start seeing the So, what happens when x is equal to 0? These first two terms are 0, you're just That's the coefficient on this term right And, you know the formula for the vertex, So, this is 3 minus 6 is negative 3 minus 2 is equal negative 5, and that actually
Is minus 6 and then minus 2, and then minusĢ.
SOLVE FOR DOMAIN AND RANGE CALCULATOR PLUS
Squared, which is just 1, minus, or I should say plus 6 times negative 1 which Negative 1? So, this is going to be 3 times negative 1 Which is 4, plus 6 times negative 2, which is 6 times negative 2, Two? Then f of x is 3 times negative 2 squared, So, let's try, well this the values we'veīeen trying the last two videos. Lets try some x values and lets see what f It comes straight out of the quadratic formula, which you get from completing the Negative b over 2a is the formula for it. There's other ways to directly compute the To calculate the vertex exactly, but let's see how we can This and maybe get a sense of its vertex. Has a shape like this, it won't take on any valuesīelow its vertex when it's upward opening, and it won't take on any values above Right over here, it is a quadratic- you might already know And, if you're familiar with quadratics- and that's what this function is I'm going to try to graph this function right over here. On a graph, it's a set of all the possible y values.
SOLVE FOR DOMAIN AND RANGE CALCULATOR SERIES
Now, the range, at least the way we'veīeen thinking about it in this series of videos- The range is set of possible, So, you take any real numberĪnd you put it here, you can square it, multiply it by 3, It's pretty muchĮverything but complex numbers. Numbers that you know of, they are part of When you first learn them, called imaginary numbersĪnd complex numbers. There is a class of numbers, that are a little bit bizarre You know, aren't all numbers real? You may or may not know that And, for those of you who might say, well, Of valid inputs, the set of inputs over which this function So essentially any number if we're talkingĪbout reals when we talk about any number. Square it, multiply it by 3, then add 6 times that real numberĪnd then subtract 2 from it. What is a set of all of the valid inputs, or all of the valid x valuesįor this function? And, I can take any real number, Determine the domain and range of the function f of x is equal toģx squared plus 6x minus 2.
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