the function f is defined as the follows
f(x)={x+6 if -5 less than or equal to
x < 1
{9 if x = 1
{-x+5 if x > 1
a. find the domain of the function f is?
b. locate any intercepts; if any
please show work
It would be great if you could somehow edit the function / math part of the problem because I do not understand if you are talking about "if less than or equal to -5" or "x<1" or "if -5 less than or equal to x<1"
Thanks a lot and Happy New Year
x+6=> if -5 less or equal to x < 1
9=> if x=1
-x+5=> if x>1
Sorry, still learing exactly how to post questions with the right signs the right way.
a. To find the domain of the function f, we need to determine the set of all values of x for which f(x) is defined.
Looking at the given piecewise definition of f(x), we can see that there are no specific restrictions on the values of x. The function is defined for all real numbers.
Therefore, the domain of the function f is all real numbers: (-∞, +∞).
b. To locate any intercepts of the function f, we are looking for the points where the function intersects the x-axis (x-intercepts) or the y-axis (y-intercepts).
x-intercept:
The x-intercept occurs when the value of f(x) is equal to 0. To find it, we set f(x) = 0 and solve for x.
For the piecewise definition given, there is no equation where f(x) = 0. Therefore, there are no x-intercepts.
y-intercept:
The y-intercept occurs when x = 0. To find it, we substitute x = 0 into the function f(x) and calculate the corresponding value.
f(0) = (0+6) = 6
Therefore, the y-intercept of the function f is (0, 6).
In summary:
a. The domain of the function f is (-∞, +∞), which includes all real numbers.
b. There are no x-intercepts. The y-intercept is (0, 6).