10. Function \( g ( x ) \) is obtained when the function \( f ( x ) = 3 ^ { x } \) is reflected over the \( y \) -axis and shifted down \( 4 \) Determine the equation for \( g ( x ) \) .
Pregunta
Answer
g(x) = 3\(^{- x}\) - 4
Related Questions
Q:
(a) Find \(\frac { f ( x + h ) - f ( x ) } { h }\) for \(f ( x ) = x ^ { 2 } - 6 x\) and hence show that \(f ^ { \prime } ( x ) = 2 x - 6\) .
(b) Use the factoring \(f ( x ) = x ( x - 6 )\) to find the \(x\) -intercepts of \(y = f ( x )\) , then sketch it.
(c) Find the gradients of the tangents at these two \(x\) -intercepts.
(d) Show that the tangent is horizontal at the point where \(x = 3\) .
Q:
A landscaper is constructing a rectangular garden bed. Three of the sides are to be fenced using \(40\) metres of fencing, while an existing wall will form the fourth side of the rectangle.
(a) Let \(x\) be the length of each of the two sides perpendicular to the wall. Show that the side parallel to the wall will have length \(( 40 - 2 x )\) metres.
(b) Show that the area of the garden bed is \(A = 40 x - 2 x ^ { 2 }\) .
(c) Find \(\frac { d A } { d x }\) , and hence find the value of \(x\) at which \(A\) attains its maximum value.
(d) Find the maximum area of the garden bed.