Question 5: (August 2023 ) The function \( G(m) \) represents the amount of gasoline consumed by a car traveling \( m \) miles. An appropriate domain for this function

15. which one of the following is the range of \( f(x)=x^{\frac{-2}{3}} \) ? \( \begin{array}{l}\text { A. IR } \backslash\{0\} \quad B .(0, \infty) \quad C .(-\infty, 0) \quad D . \mathbb{R}\end{array} \)

Sketch on the same set of axes the graphs of \( f(x)=-2 x^{2}-4 x+6 \) and \( g(x)=-2 \cdot 2^{x-1}+1 \). Clearly indicate all intercepts with the axes, turning point(s) and asymptote(s).

Mathematics Assignment for Grade 12. December 15/04/2017 E. C. Instructions: - Workout the following problems with the necessary steps with clear and legible handwriting. - Write your group number, full name with their Roll NO. 1. The number of terms in an arithmetic progression is even. The sum of the odd terms is 24. If the sum of even terms is 30 and the last term exceeds the first by \( \frac{21}{2} \), then find the number of terms. 2. If \( a^{2}+b^{2}, a b+b c \) and \( b^{2}+c^{2} \) are in geometric progression, prove that \( a, b, c \) are also in geometric progression. 3. Let \( f(x)=\left\{\begin{aligned} 4 x, & x \geq 3 \\ x^{2}+3, & x<3\end{aligned}\right. \), find the equation of the tangent line and the normal line to the graph of \( f \) at the point \( (4,16) \). 4. Find the maximum possible area of an isosceles triangle whose perimeter is 6 m . 5. Given \( f(x)=\sqrt{12-x-x^{2}},[-4,3] \) find: a) absolute maximum. b) dbsotute-minimum.

QUESTION 3 The equation of a hyperbola is given by \( f(x)=\frac{3}{x-7}-4 \). Write down the equation of the new function that is formed when \( f \) is transformed as follows: \( 3.1 \quad \) Shift two units to the left

Linear Speed Find the linear speed for the following. 15. The second hand of a clock is 11.25 centimeters long. Find the linear speed of the tip of the second hand as it passes around the clock face. 16. The blades of a wind turbine are 85 feet. The propeller rotates at 13 revolutions per minute. Find the linear speed of the tips of the blades.