156k views
1 vote
Maths functions question

Maths functions question-example-1
User Tam Coton
by
7.9k points

1 Answer

3 votes

Answer:

a) OA = 1 unit

b) OB = 3 units

c) AB = √10 units

Explanation:

Given function:


g(x)=2^x

Part (a)

Point A is the y-intercept of the exponential curve (so when x = 0).

To find the y-value of Point A, substitute x = 0 into the function:


\implies g(0)=2^0=1

Therefore, A (0, 1) so OA = 1 unit.

Part (b)

If BC = 8 units then the y-value of Point C is 8.

The find the x-value of Point C, set the function to 8 and solve for x:


\begin{aligned}f(x) & = 8 \\\implies 2^x & = 8\\2^x & = 2^3\\\implies x &= 3\end{aligned}

Therefore, C (3, 8) so Point B is (3, 0). Therefore, OB = 3 units.

Part (c)

From parts (a) and (b):

  • A = (0, 1)
  • B = (3, 0)

To find the length of AB, use the distance between two points formula:


d=√((x_2-x_1)^2+(y_2-y_1)^2)


\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points.}

Therefore:


\implies \sf AB=√((x_B-x_A)^2+(y_B-y_A)^2)


\implies \sf AB=√((3-0)^2+(0-1)^2)


\implies \sf AB=√((3)^2+(-1)^2)


\implies \sf AB=√(9+1)


\implies \sf AB=√(10)\:\:units

Maths functions question-example-1
User Ishant Gaurav
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories