POLYNOMIAL FUNCTIONS
QUESTION
- domain and range of Y= x² +5
REMEMBER
- If the polynomial function does not contain rationals and radicals then the function doesn't have restrictions. Doesn't have restriction means that you can plug any numbers to the value of x and the domain will be all real numbers.
- Domain = all possible values of x
- Range = all possible values of y
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QUADRATIC FUNCTIONS
y = ax²+bx+c , y = a(x-h)²+k
Given : y = x² + 5
- The given function is a quadratic and its graph is parabola. I know that it opens upward because the value of a is positive.
We already know the domain and it is all real numbers
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Finding for the range:
Solution 1:
Evaluate the value of x to zero and solve for y
- y = x² + 5
- y = (0)² + 5
- y = 5 , then if it opens upward the sign will be ≥ , if it opens downward the sign will be ≤ .
domain = all real numbers
range = y ≥ 5
Solution 2:
transpose to vertex form and find the value of the k or minimun/maximun value
- y = x²+5
- y = (x+0)²+5
- get the value of k which is 5 , use the rule again .
Domain = all real numbers
Range = y ≥ 5
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FINAL ANSWER
Word form
- Domain is the set of all real numbers
- Range is greater than or equal to 5
Inequality form
- x | { x = IR }
- y | { y ≥ 5 }
Interval form
- ( -infinity , +infinity )
- ( 5 , +infinity )
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