Name: Properties of Transformations: Reflections
Uploaded: 2019-07-19
Duration: 43 min 51 s
Description: There are four types of transformation that we learn about in maths: rotation, reflection, translation, and enlargement. Here, let us learn about reflections.

Question

Represent on a graph the function

$f (x) = \{\begin{cases} 9 - x^{2} for x \in ℝ, - 3 \leq x \leq 2 \\ 2 x + 1 for x \in ℝ, 2 \leq x \leq 4 \end{cases}$

State the nature of the function.

Accepted Answer

Given $f (x) = \{\begin{cases} 9 - x^{2} for x \in ℝ, - 3 \leq x \leq 2 \\ 2 x + 1 for x \in ℝ, 2 \leq x \leq 4 \end{cases}$

When $x = 0, f (x) = 9 - 0^{2} = 9$ , $f (1) = 9 - 1^{2} = 8$

and $x = - 3, f (x) = 9 - {(- 3)}^{2} = 0$

When $x = 2, f (x) = 5$ and $x = 4, f (x) = 2 (4) + 1 = 9$ then $f (x)$ is a straight line.

Now plot the graph using the above values

A function is a relation that uniquely associates members of one set with members of another set.

We can see that the input value shown has unique output values. This means that the graph represent a function.

The horizontal line test checks if a function is one-to-one. If a horizontal line passes through a graph more than once, the function has more than one x value for at least one y value, so it cannot be one-to-one.

Any function $f (x)$ is defined on set $X$ is said to be one one if the horizontal line cuts the graph of $f (x)$ at most one point.

The horizontal line intersecting the graph at more than one point

A many-one function has one output value for each input value but each output value can have more than one input value.

Hence, the given function is many one function.

Represent on a graph the function

$f (x) = \{\begin{cases} 9 - x^{2} for x \in ℝ, - 3 \leq x \leq 2 \\ 2 x + 1 for x \in ℝ, 2 \leq x \leq 4 \end{cases}$

State the nature of the function.

Important Questions on Functions

Learn and Prepare for any exam you want !

Represent on a graph the function fx=9-x2 for x∈ℝ, -3≤x≤22x+1 for x∈ℝ, 2≤x≤4 State the nature of the function.

Important Questions on Functions

Learn and Prepare for any exam you want !

Represent on a graph the function

$f (x) = \{\begin{cases} 9 - x^{2} for x \in ℝ, - 3 \leq x \leq 2 \\ 2 x + 1 for x \in ℝ, 2 \leq x \leq 4 \end{cases}$

State the nature of the function.