EXERCISE 3 1. For each function below: $$ \begin{array}{ll} ext { (1) } \ ext { Draw a neat sketch graph indicating the coordinates of the } \ ext { intercepts with the axes, the coordinates of the turning point and } \ ext { the equation of the axis of symmetry. } \ ext { Determine the domain and range. } \ ext { (2) } \ ext { Determine the values of } x ext { for which the graph increases and } \ ext { decreases. } \ ext { (4) Determine the maximum or minimum value of the graph. } \ ext { (a) } f(x)=(x+1)^{2}-4 & ext { (b) } f(x)=-(x+1)^{2}+4 \ ext { (c) } f(x)=(x-1)^{2}-4 & ext { (d) } f(x)=-(x-1)^{2}+4 \ ext { (e) } f(x)=(x-2)^{2}-1 & ext { (f) } g(x)=(x+1)^{2}+2 \ ext { (g) } g(x)=-(x+1)^{2}-2 & ext { (h) } g(x)=(x-2)^{2}-9 \ ext { (i) } g(x)=2(x+1)^{2}-2 & ext { (j) } g(x)=(x-4)^{2}-2\end{array} $$

Question

EXERCISE 3 1. For each function below: $$ \begin{array}{ll}	ext { (1) } \ 	ext { Draw a neat sketch graph indicating the coordinates of the } \ 	ext { intercepts with the axes, the coordinates of the turning point and } \ 	ext { the equation of the axis of symmetry. } \ 	ext { Determine the domain and range. } \ 	ext { (2) } \ 	ext { Determine the values of } x 	ext { for which the graph increases and } \ 	ext { decreases. } \ 	ext { (4) Determine the maximum or minimum value of the graph. } \ 	ext { (a) } f(x)=(x+1)^{2}-4 & 	ext { (b) } f(x)=-(x+1)^{2}+4 \ 	ext { (c) } f(x)=(x-1)^{2}-4 & 	ext { (d) } f(x)=-(x-1)^{2}+4 \ 	ext { (e) } f(x)=(x-2)^{2}-1 & 	ext { (f) } g(x)=(x+1)^{2}+2 \ 	ext { (g) } g(x)=-(x+1)^{2}-2 & 	ext { (h) } g(x)=(x-2)^{2}-9 \ 	ext { (i) } g(x)=2(x+1)^{2}-2 & 	ext { (j) } g(x)=(x-4)^{2}-2\end{array} $$

UpStudy AI · Accepted Answer

To solve this exercise, we need to analyze each function given and determine the following: 1. Sketch the graph indicating the coordinates of the intercepts with the axes, the coordinates of the turning point, and the equation of the axis of symmetry. 2. Determine the values of $$ x $$ for which the graph increases and decreases. 3. Determine the maximum or minimum value of the graph. Let's start with function (a) $$ f(x) = (x+1)^2 - 4 $$. 1. Sketch the graph: The graph of $$ f(x) = (x+1)^2 - 4 $$ is a parabola that opens upwards. The vertex of the parabola is at $$ x = -1 $$ and $$ f(-1) = -4 $$. The axis of symmetry is the vertical line $$ x = -1 $$. 2. Determine the values of $$ x $$ for which the graph increases and decreases: The graph increases when $$ x > -1 $$ and decreases when $$ x < -1 $$. 3. Determine the maximum or minimum value of the graph: The maximum value of the graph is $$ f(-1) = -4 $$. Now, let's analyze the rest of the functions in the same manner. For each function, sketch the graph showing intercepts, turning point, and axis of symmetry. Determine the domain and range. Identify where the graph increases and decreases, and find the maximum or minimum value. Function (a): $$ f(x) = (x+1)^2 - 4 $$ - Vertex at $$ x = -1 $$, $$ f(-1) = -4 $$ - Axis of symmetry: $$ x = -1 $$ - Increases for $$ x > -1 $$, decreases for $$ x < -1 $$ - Minimum value: $$ -4 $$ Function (b): $$ f(x) = -(x+1)^2 + 4 $$ - Vertex at $$ x = -1 $$, $$ f(-1) = 4 $$ - Axis of symmetry: $$ x = -1 $$ - Decreases for $$ x > -1 $$, increases for $$ x < -1 $$ - Maximum value: $$ 4 $$ Function (c): $$ f(x) = (x-1)^2 - 4 $$ - Vertex at $$ x = 1 $$, $$ f(1) = -4 $$ - Axis of symmetry: $$ x = 1 $$ - Increases for $$ x > 1 $$, decreases for $$ x < 1 $$ - Minimum value: $$ -4 $$ Function (d): $$ f(x) = -(x-1)^2 + 4 $$ - Vertex at $$ x = 1 $$, $$ f(1) = 4 $$ - Axis of symmetry: $$ x = 1 $$ - Decreases for $$ x > 1 $$, increases for $$ x < 1 $$ - Maximum value: $$ 4 $$ Function (e): $$ f(x) = (x-2)^2 - 1 $$ - Vertex at $$ x = 2 $$, $$ f(2) = -1 $$ - Axis of symmetry: $$ x = 2 $$ - Increases for $$ x > 2 $$, decreases for $$ x < 2 $$ - Minimum value: $$ -1 $$ Function (f): $$ g(x) = (x+1)^2 + 2 $$ - Vertex at $$ x = -1 $$, $$ g(-1) = 2 $$ - Axis of symmetry: $$ x = -1 $$ - Increases for all $$ x $$ - Minimum value: $$ 2 $$ Function (g): $$ g(x) = -(x+1)^2 - 2 $$ - Vertex at $$ x = -1 $$, $$ g(-1) = -2 $$ - Axis of symmetry: $$ x = -1 $$ - Decreases for all $$ x $$ - Maximum value: $$ -2 $$ Function (h): $$ g(x) = (x-2)^2 - 9 $$ - Vertex at $$ x = 2 $$, $$ g(2) = -9 $$ - Axis of symmetry: $$ x = 2 $$ - Increases for $$ x > 2 $$, decreases for $$ x < 2 $$ - Minimum value: $$ -9 $$ Function (i): $$ g(x) = 2(x+1)^2 - 2 $$ - Vertex at $$ x = -1 $$, $$ g(-1) = -2 $$ - Axis of symmetry: $$ x = -1 $$ - Increases for all $$ x $$ - Minimum value: $$ -2 $$ Function (j): $$ g(x) = (x-4)^2 - 2 $$ - Vertex at $$ x = 4 $$, $$ g(4) = -2 $$ - Axis of symmetry: $$ x = 4 $$ - Increases for $$ x > 4 $$, decreases for $$ x < 4 $$ - Minimum value: $$ -2 $$

EXERCISE 3

For each function below:

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Pre Calculus Questions

EXERCISE 3 For each function below: