Complete the following exercises on differential calculus with analytical geometry for automotive engineering: AC10. Locate the following points in...

Complete the following exercises on differential calculus with analytical geometry for automotive engineering:
AC10. Locate the following points in the coordinate system and, using the vertical line test, determine if the graph belongs to an “x” function:
Table 15
x √5 −√5 0 0
y 0 0 √5 −√5
Table 16
x 1 2 3 4
y 0 1 2 3
AC11. Complete the table with the graphs of given standard functions, and write their respective domains and ranges:
Table 17
(x)=c f(x) = x f(x) = x2 f(x) = x3
f(x) = 1/x ????????(????????) = √???????? f(x) = ln(x) f(x) = ex
f(x)=sen(x) f(x)=cos(x) f(x)=tan(x) f(x) = |x|
AC12. If h(x)=3x2 -15x +9, indicate the possible functions f(x) and g(x) if h(x) = f(x) +g(x) or h(x) = g(x) - f(x), h(x) = f(x)g(x), h(x) = (f ° g)(x). If h(x) = (g(x)/f(x)), indicate the possible functions f(x) and g(x).
AC13. Let ????????(????????) = √???????? − 5 and g(x) = 4x2+x. Determine (f ° g)(x) and its respective domain.
AC14. Determine the domain and range in the following function cases.
AC15. Indicate the domain and range of the functions graphed below:
Figure 107
AC16. Let f(x) be the function of the graph. Determine:
The maximum and minimum values of f(x).
The intervals where f(x) is increasing and decreasing.
The intervals where f(x) is concave up and concave down.
The inflection points of f(x).