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Domain and Range

QuestionAnswer
What is the name of this function? f(x) = 10 Constant Function
What is the name of this function f(x) = ax+b Linear Function
Why can't a=o in the linear function? Because if a is o, then the linear function would turn into a constant function.
What is the name of the graph of a linear function? Diagonal line
What is the name of the graph of a constant function? Horizontal line
What is the name of this function f(x)= x Identity function
What is the name of the graph of an identity function? Diagonal line
What type of function is an identity function? It is a special type of linear function.
What is the name of this function f(x)= ax2+bx+c Quadratic function
What is the name of the graph of a quadratic function? Parabola
Why can't a=0 in a quadratic function? a can't equal zero because quadratic function will turn into a linear function
If the leading coefficient is positive how will the graph of a quadratic function look? the parabola will open up meaning the lowest point of the parabola is the vertex and to use [y-coordinate of the vertex, infinity)
If the leading coefficient is negative how will the graph of a quadratic function look? parabola will open down and the vertex is the highest point. The range will follow the format of (-infinity, y-coordinate of the vertex]
ex. f(x)=2x2+12+30. Find the domain and range. Domain: -infinity, infinity Range: [12, infinity)
How do you find y- intercept set the x's to 0
how do you find x-intercept set the y to o
when is the vertex a maximum? when the leading coeffiecient is negative and goes down
When is the vertex a minimum? when the leading coefficient is positive and goes up
when do you use the from [y-coordinate of vertex, i infinity)? when the leading coefficient is positive and goes up
when do you use the form [-infinity, y-coordinate of vertex) when the leading coefficient is negative and goes down
ex. of a quadratic equation. x2+ 15x+ 15. Solve. Have to find answer.
What is the name of this function ax3+ bx2+cx+d Cubic function
What is the range and domain of a cubic function? All reals because the graph representation goes up and down and left and right infintely
What is another name for a linear function? 1st degree polynomial
What is another name for a quadratic function? 2nd degree polynomial
What is the name of this function 3squareroot ax+b radical of an odd index
What is the name of this function squareoot ax+b radical of an even index
How do you find the domain of a radical of an odd index you look at the radicant and simply find the domain of it.
How do you find the domain of a an odd radical with a linear radicant? if it is linear then the domain will always be all reals
How do you find the domain of an odd radical with a quadratic radicant? if it is quadratic then then the domain will be found exactly how the domain of a regular quadratic function is.
How do you find range of an odd radical find range of the radicant then apply the radical. for a linear it will still be infinity. for a quadratic it might not be.
ex. of a linear equation under odd radical. 5squareroot 2x+3. Find range and domain D: (-infinity, infinity) R: (-infinity, infinity)
ex. of a quadratic equation under odd radical. squareroot7 2x2+12x+30 D: all reals R: [7 squareroot 12, infinity)
How to find the domain of an even radical? you must take the radicant and set it greater and equal to zero and solve.
What if it is specifically a linear equation under the even radical function? you will still set it greater or equal to zero and then what x is greater or equal to will be the lower bound with infinity as the upperbound.
Wht if it is specifically a quadratic function under the even radical function? Will set greater than 0 and find the zeros. They are called critical points. Then you have to do the chart to find whether the products of those critical points are consistent with the greater than in the equation
Created by: prosper