Pretend the parentheses are absolute value bars.
Find the domain and range of
y = -1/4(x) + 1
How would I figure this out? Thank you so much!
|x| is always >/= 0
If x = 0
y = 1
If |x| > 0 (that is a domain of all real x, positive or negative)
y < 1
so
domain is all real x
and
range is y </= 1
graph it
To find the domain and range of the given function, we need to consider two things: the restrictions on the input (x) values and the possible output (y) values.
1. Domain:
The domain represents all possible input values for the function. In this case, there are no restrictions on the input (x) values. Therefore, the domain is all real numbers (-∞, +∞).
2. Range:
The range represents all possible output values for the function. To find the range, we can look at the behavior of the function.
The given function is a linear equation in the form y = mx + b, where m represents the slope and b represents the y-intercept.
In this case, the equation is y = -1/4(x) + 1. The slope of the line is -1/4, which means the line decreases by -1/4 for every unit increase in x.
To determine the range, we need to consider the behavior of the line. Since the slope is negative, the line is decreasing as we move from left to right. Therefore, the range consists of all y-values that the line can attain.
In this case, the line can take any real value for y, since there are no restrictions. So, the range is also all real numbers (-∞, +∞).
Therefore, the domain and range of the given function y = -1/4(x) + 1 are:
Domain: All real numbers (-∞, +∞)
Range: All real numbers (-∞, +∞)