Cubic Functions Grade 12 Questions and Answers pdf

Cubic Functions Grade 12 Questions and Answers pdf Download Cubic functions are an essential topic in high school mathematics, particularly in Grade 12, where students dive deeper into the realm of algebra and functions. These functions, characterized by their cubic polynomials, offer a rich landscape for exploration, providing insights into various real-world phenomena and mathematical concepts. In this blog post, we’ll delve into some Grade 12-level questions related to cubic functions, along with detailed answers to help students grasp these concepts effectively.

Question 1: Determine the end behavior of the cubic function f(x)=x3−2×2−x+2f(x)=x3−2x2−x+2.

Answer: To analyze the end behavior of a cubic function, we examine the leading term, which in this case is x3x3. As $x$ approaches negative infinity, x3x3 also approaches negative infinity, indicating that the graph of the function will trend downwards to the left. Similarly, as $x$ approaches positive infinity, x3x3 approaches positive infinity, suggesting that the graph will trend upwards to the right. Therefore, the end behavior of the function f(x)=x3−2×2−x+2f(x)=x3−2x2−x+2 is as follows:

• As $x$ approaches negative infinity, $f(x)$ approaches negative infinity.
• As $x$ approaches positive infinity, $f(x)$ approaches positive infinity.

Question 2: Find the $x$-intercepts of the cubic function g(x)=x3−6×2+9xg(x)=x3−6x2+9x.

Answer: The $x$-intercepts of a function correspond to the points where the graph intersects the $x$-axis, i.e., where $f(x)=0$. To find these points for the function g(x)=x3−6×2+9xg(x)=x3−6x2+9x, we set $g(x)=0$ and solve for $x$:

x3−6×2+9x=0x3−6x2+9x=0

Factoring out $x$, we get:

x(x2−6x+9)=0x(x2−6x+9)=0

Further factoring the quadratic term inside the parentheses:

$x(x-3)(x-3)=0$

Setting each factor equal to zero, we find the roots:

$x=0\text{and}x=3$

So, the $x$-intercepts of the function g(x)=x3−6×2+9xg(x)=x3−6x2+9x are $x=0$ (with a multiplicity of 1) and $x=3$ (with a multiplicity of 2).

Question 3: Determine the critical points of the cubic function h(x)=x3−12x+8h(x)=x3−12x+8.

Answer: Critical points occur where the derivative of a function is either zero or undefined. To find the critical points of the function h(x)=x3−12x+8h(x)=x3−12x+8, we first take the derivative h′(x)h′(x) and then solve for $x$ where h′(x)=0h′(x)=0:

h′(x)=3×2−12h′(x)=3x2−12

Setting h′(x)h′(x) equal to zero:

3×2−12=03x2−12=0

x2−4=0x2−4=0

$(x-2)(x+2)=0$

So, $x=2$ and $x=-2$ are the critical points of the function h(x)=x3−12x+8h(x)=x3−12x+8.

These questions and answers provide a glimpse into the world of cubic functions, showcasing their significance in Grade 12 mathematics curriculum. By mastering concepts related to cubic functions, students not only enhance their algebraic skills but also develop a deeper understanding of functions and their properties, paving the way for more advanced mathematical explorations.

Cubic Functions Grade 12 Notes

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