Given no other restrictions, what are the domain and range of the following funtction? f(x)=x^2-2x+2
2 answers:
Answer: Domain of the given function is all real numbers.
Range of the given function is {y | y>=1}
Step-by-step explanation:
The given function is a polynomial and the domain of any polynomial is all the real numbers because for any value of x, the function will have some value.
Hence, the domain will be all real numbers.
Range is the set of y values for which the function is defined.
This is a polynomial and to find the range, we will simplify the polynomial.
Therefore, for any value of x, f(x) ≥ 1
Hence, the range becomes {y | y ≥ 1}
You might be interested in
The slope of the function, f(x) can be determined by choosing two sets of ordered pairs from the table and substituting their values into the slope formula.
Let (x1, y1) = (0, -1)
(x2, y2) = (1, 7)
Plug these values into the slope formula:
m = (y2 - y1)/(x2 - x1)
m = [7 - (-1)] / [1 - 0]
m = (7 + 1) / 1
m = 8/1 or 8.
Therefore, the slope of f(x), m = 8.
The y-intercept of the function, f(x) is given by (0, -1), as it is the point on the graph where it crosses the y-axis. It is also the value of y when x = 0.
The equation of the linear function, f(x) is:
f(x) = 8x - 1.
Given the slope-intercept form, y = mx + b, where m represents the slope of the line, and b represents the y-intercept:
The function, g(x) = 3x - 2 has a slope of 3, and y-intercept of -2.
Comparing the slope and y-intercept of the two functions, f(x) and g(x):
The slope of f(x), m = 8 is greater and steeper than the slope of g(x), m = 3. The y-intercept of f(x), b = -1 is greater than the y-intercept of g(x), b = -2.
Attached is a screenshot of the graph of both lines, including their y-intercepts. The blue line is g(x) = 3x - 2, and the red line is f(x) = 8x - 1.
Please mark my answers as the Brainliest if you find this helpful :)
Let (x1, y1) = (0, -1)
(x2, y2) = (1, 7)
Plug these values into the slope formula:
m = (y2 - y1)/(x2 - x1)
m = [7 - (-1)] / [1 - 0]
m = (7 + 1) / 1
m = 8/1 or 8.
Therefore, the slope of f(x), m = 8.
The y-intercept of the function, f(x) is given by (0, -1), as it is the point on the graph where it crosses the y-axis. It is also the value of y when x = 0.
The equation of the linear function, f(x) is:
f(x) = 8x - 1.
Given the slope-intercept form, y = mx + b, where m represents the slope of the line, and b represents the y-intercept:
The function, g(x) = 3x - 2 has a slope of 3, and y-intercept of -2.
Comparing the slope and y-intercept of the two functions, f(x) and g(x):
The slope of f(x), m = 8 is greater and steeper than the slope of g(x), m = 3. The y-intercept of f(x), b = -1 is greater than the y-intercept of g(x), b = -2.
Attached is a screenshot of the graph of both lines, including their y-intercepts. The blue line is g(x) = 3x - 2, and the red line is f(x) = 8x - 1.
Please mark my answers as the Brainliest if you find this helpful :)