1Identify the interval where the function represented by the following graph is increasing. (Assume the graph shows a function with intervals of increase and decrease.)
2For the given piecewise function graph, identify the number(s) at which f has a relative minimum and the corresponding relative minimum value(s). (Assume the graph shows a piecewise function with sharp corners.)
3Determine whether the function f(x) = x⁵ - x⁴ is even, odd, or neither.
4Determine whether the function f(x) = -2x⁵ + x³ is even, odd, or neither.
5Using possible symmetry, determine whether the given graph represents an even function, an odd function, or a function that is neither even nor odd. (Assume the graph shows a function with no apparent symmetry.)
6Evaluate the piecewise function g(x) at the given value: g(x) = { x² - 6 / x + 6 if x ≠ -6; x + 2 if x = -6 }. Find g(5).
7A car rental company charges $118 for the first day and $68 for each additional or partial day. Let S(x) represent the cost of renting a car for x days. Calculate the value of S(5.5).
8Find and simplify the difference quotient f(x + h) - f(x) / h for the function f(x) = 1 / 7x.
9The function h(x) = -√(x + 2) - 1 is a transformation of the standard square root function f(x) = √x. Describe the transformations applied.
10The function g(x) = - ³√(x + 8) is a transformation of the standard cube root function f(x) = ³√x. Describe the transformations applied.
