Problem
1. Given $f(x)=x^{2}+3 x-7$, evaluate $f(2)$. 0 2. State the domain and range for the given function.2 Domain: Range: 3. Write the equation for a parabola that is vertically stretched by a factor of 3 , reflected in the $\mathrm{x}$-axis and translated right 2 units. 4. State whether each of the following represents a linear, quadratic or exponential function.2 a) $y=2 x-1$ b) $y=(1 / 2)^{x}$ PART C: FULL SOLUTIONS REOUIRED[21 Marks] 1. Expand and simplify. $(3 y-2)(y+1)-2(y-4) 3$ 2. Factor each expression. a) $9 x^{2}-81$ b) $-8 x^{2}+44 x-48$ 3. Solve by factoring or using the quadratic formula a) $x^{2}-5 x+6=02$ b) $2 x^{2}+3 x-1=0$ MCF3M1 Culminating Task June 2023 Page 2 of 3
Solution
Step 1 ：\(f(2) = (2)^2 + 3(2) - 7 = 4 + 6 - 7 = \boxed{3}\)
Step 2 ：Domain: \(\boxed{(-\infty, \infty)}\)
Step 3 ：Range: \(\boxed{(-\infty, \infty)}\)
Step 4 ：3. \(y = -3(x-2)^2 = \boxed{-3(x^2-4x+4)}\)
Step 5 ：4a) \(y = 2x - 1\) is a \(\boxed{\text{linear}}\) function.
Step 6 ：4b) \(y = (\frac{1}{2})^x\) is a \(\boxed{\text{exponential}}\) function.
