Question

Which of the following statements is/are correct for the above given figure?

1.For all the function A, B and C, domain is R and Range is $(0,\infty )$.

2.Function B is a graph for $F\left(x\right)=a^x,a>1,xϵR$.

3.Function A is a graph for $F\left(x\right)=a^{x}0<a<1,xϵR$

4.Function C is a graph for $F\left(x\right)=a^x,a<0,xϵR$

5.If the graph of B is $5^x$, then the graph of A is $y=8^x$ and the graph of C is

$y=2^x$ (you have to choose graph from $2^x,8^{x}and{5}^x)$

6.If the graph of B is $5^x$, then the graph of A is $y=2^x$ and the graph of C is

$y=8^x$ (you have to choose graph from $2^x,8^{x}and{5}^x)$

• A. Only 1, 3, 6
• B. Only 1, 2, 5
• C. Only 1, 4, 5
• D. Only 3, 6

Answer 1

The correct option is B

Only 1, 2, 5

Statement 1: For all the functions A, B and C, Domain is R and Range is $(0,\infty )$

We can clearly see from the graph that x can take any value. So domain is R.

Nowhere graph is below the y - axis. So, all three graphs give positive values. So, Range of the graph is $(0,\infty )$

Statement 1 is correct.

Statement 2: Function B is a graph for $F\left(x\right)=a^x,a>1xϵR$ the graph of Function $F\left(x\right)=a^x,a>1$ is

So, statement 2 is correct.

Statement 3: Graph of $F\left(x\right)=a^x$

$0<a<1xϵR$

So, statement 3 is incorrect.

Statement 4: Graph of $F\left(x\right)=a^x,a<0,xϵR$

It cannot be any of the graph shown in the question because when $a<0$ and x = -2, F(x)

will not be defined. {For it to be define a should be greater than or equal to zero}

For all the values of x, $a^x$ is NOT defined when $a<0$.

So, any of the above graph is NOT a function of $a^x$ when $a<0xϵR$.

So, statement 4 is incorrect.

Statement 5: If graph B is $f\left(x\right)=5^x$

Then the value of a$\left[f\right(x)=a^x]$ for the graph A should be more than 5 and value of a for graph C should less than 5because for positive x values graph A is steeper than graph B $\&$ C.

So, rate of increases of graph A is faster than graph B.

Rate of increases of graph B is faster than graph C.

If graph B is $f\left(x\right)=5^x$

Graph A is $f\left(x\right)=8^x$, graph C is $f\left(x\right)=2^x$

So statement 5 is correct

Statement 6:

: If graph B is $f\left(x\right)=5^x$

Then the value of $a\left[f\right(x)=a^x]$ for the graph A should be more than 5 and value of a for graph C should less than 5 because for positive x values graph A is steeper than graph B $\&$ C.

So, rate of increases of graph A is faster than graph B.

Rate of increases of graph B is faster than graph C.

If graph B is $f\left(x\right)=5^x$

Graph A is $f\left(x\right)=2^x$, graph C is $f\left(x\right)=8^x$ is NOT correct.

So statement 6 is incorrect.

Only statement 1, 2 $\&$ 5 are correct.