Which graph is the graph of this function?

Option 3. is the answer.

Step-by-step explanation:

The given function is represented by the f(x) = 3 if 0 ≤ x < 3

This means the given function is defined for the values between grater than equal to 0 and less than 3.

Similarly, f(x) = 5 -x if 3 ≤ x ≤ 5

So the function is defined for the values of x greater than equal to 3 and less than equal to 5.

Graph 1 - It is graphed for the values of 1 ≤ x ≤ 3.

Therefore, this is not the graph for the given function.

Graph 2 - This is the graph for a function between 0 ≤ x ≤ 3 and 4 ≤ x ≤ 5

Therefore, this is not for the given function.

Graph 3 - This graph shows the function defined between 0 ≤ x < 3 and 3 ≤ x ≤ 6

Therefore, this the correct graph given for the function.

Graph 4 - The given function in the graph has been graphed for 1 ≤ x ≤ 2 and 1 ≤ x ≤ 3

Therefore, it's an incorrect graph for the given function f(x).

Option 3. is the answer.

no oblique asymptote

step-by-step explanation:

to find the oblique asymptote of f(x)

here numerator has degree 1 and denomintor degree 2

degree of numerator < degree of denominator

hence there is no oblique asymptote

when the degree of the denominator > that of the numerator, we saw that the value in the denominator got so much bigger, so quickly,   giving us a horizontal asymptote of the x-axis. or we can write

f(x) = a polynomial of x + a proper fraction.

in this case only we have oblique asymptotes but not when numerator has less degree.