Function Calculator

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**Step 1 :**

**Step 2 :**

The relation between input and output is defined by **Function**, if the input of the function changes, then its resultant has also changed. **Function Calculator** is a input output calculator that will help us to graph a function. It is a linear function calculator if the input is a quadratic function, then it calculates the x-intercept, y-intercept and vertex. If the input is linear function, then it calculates the x-intercept, y-intercept and slope. It called as function tables input output calculator.

Below is given a default function, click "Graph". It calculates x-intercept, y-intercept, slope and then plot the graph.

Below is given a default function, click "Graph". It calculates x-intercept, y-intercept, slope and then plot the graph.

Observe the given linear function.

Plug in different values for x and find the value for y and then list all the coordinates and plot it on graph.

Plot the graph for the function: f(x) = 2x + 1

**Step 1 :**Given function: f(x) = y = 2x + 1

**Step 2 :**if x = 0, then

y = 2(0) + 1 = 1

y = 1

if x = 1, then

y = 2(1) + 1 = 3

y = 3

if x = 2, then

y = 2(2) + 1 = 5

y = 5

if x = -1, then

y = 2(-1) + 1 = -1

y = -1

So, the coordinates are (0, 1), (1, 3), (2, 5) and (-1, -1)

**Answer :**Plot the graph for the function: f(x) = x + 12

**Step 1 :**Given function: f(x) = y = x + 12

**Step 2 :**if x = -10, then

y = -10 + 12 = 2

y = 2

if x = 10, the

y = 10 + 12 = 22

y = 22

if x = 20, then

y = 20 + 12 = 32

y = 32

if x = 30, then

y = 30 + 12 = 42

y = 42

So, the coordinates are (-10, 2) (10, 22), (20, 32) and (30, 42)

**Answer :**An engineer of a manufacturing company has designed a model in the shape of a right triangle. The smaller side of a triangle is equal to $\frac{3} {5} $ of its largest side. Also the length of the second largest side of a triangle is 8 cm. What is the sum of the smallest and the largest sides of the model together. Also plot graph for the function.

**Step 1 :**Given model in the shape of a right triangle. And the relation between the sides of a triangle is given below:

(Hypotenuse)$^2 $ = (Base) $^2 $ + (Altitute) $^2 $

**Step 2 :**Let 8 cm be the altitude of the triangle, then

H$^2 $ = B$^2$ + 8$^2 $ ….. (1)

(where H and B represent Hypotenuse and base of the triangle respectively)

Or H = $\sqrt{B^2+64} $ (Which is required function)

Put B = 1 and -1 then H = 8.06 (approx)

Put B = 2 and -2 then H = 8.24 (approx)

Put B = 3 and -3 then H = 8.25 (approx)

Put B = 6 and -6 then H = 10

Since smaller side = $\frac{3} {5} $ (largest side)

Values B = 6 and H = 10 completely satisfy equation (1). The sides of the model are 6, 8 and 10.

Sum of smallest and largest sides = 6 + 10 = 16.

**Answer :**Sum of smallest and largest sides = 16 cms.