Fill in the blank: To obtain the graph of y=2x+0.2, you can start with the graph of y=2x and translate it ___________.
A. 0.2 units to the right
B. 0.2 units to the left
C. 0.2 units up
D. 0.2 units down
Which of these functions has a domain of all real numbers except x=4.1?
A. y=2.5x−4.1+2.8
B. y=2.8x+4.1−2.5
C. y=4.1x−2.8+2.5
D. y=4.1x−2.5+2.8
To obtain the graph of y=2x+0.2, you can start with the graph of y=2x and translate it 0.2 units up.
Explanation: To translate a graph vertically, you add or subtract a constant value to the function. In this case, the constant value is 0.2, and since it is positive, we add it to the original function. This shifts the entire graph upwards by 0.2 units.
Now, let's consider the second question.
The function with a domain of all real numbers except x=4.1 is:
C. y=4.1x−2.8+2.5
Explanation: The domain of a function represents all possible inputs (x-values) for which the function is defined. In this case, we need to find the function that has all real numbers as its domain except for x=4.1, which means we need to find the function where x can take any value except 4.1.
Looking at the options, the function y=4.1x−2.8+2.5 satisfies this condition. The x-term of the function, 4.1x, is present, but it is added or subtracted to other terms, so it does not affect the domain. That is why this function has a domain of all real numbers except x=4.1.
recall that
to translate a graph h units to the right, replace x with (x-h)
to translate it up by k units, replace y with (y-k)
as written, all of those functions are polynomials, with a domain of all reals. If you want the domain to exclude x=4.1, then you need a rational function with (x-4.1) as a factor in the denominator.
Learn to write math with "/" symbols for fractions, and parentheses to group terms. I suspect that the way you posted the functions is not how they appeared in your assignment.