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,∞).
2.Function B is a graph for F(x)=ax,a>1,xϵR.
3.Function A is a graph for F(x)=ax0<a<1,xϵR
4.Function C is a graph for F(x)=ax,a<0,xϵR
5.If the graph of B is 5x, then the graph of A is y=8x and the graph of C is
y=2x (you have to choose graph from 2x,8x and 5x)
6.If the graph of B is 5x, then the graph of A is y=2x and the graph of C is
y=8x (you have to choose graph from 2x,8x and 5x)
Only 1, 2, 5
Statement 1: For all the functions A, B and C, Domain is R and Range is (0,∞)
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,∞)
Statement 1 is correct.
Statement 2: Function B is a graph for F(x)=ax, a>1 x ϵ R the graph of Function F(x)=ax,a>1 is
So, statement 2 is correct.
Statement 3: Graph of F(x)=ax
0<a<1 x ϵ R
So, statement 3 is incorrect.
Statement 4: Graph of F(x)=ax,a<0,x ϵ R
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, ax is NOT defined when a<0.
So, any of the above graph is NOT a function of ax when a<0 x ϵR.
So, statement 4 is incorrect.
Statement 5: If graph B is f(x)=5x
Then the value of a[f(x)=ax] 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(x)=5x
Graph A is f(x)=8x, graph C is f(x)=2x
So statement 5 is correct
Statement 6:
: If graph B is f(x)=5x
Then the value of a[f(x)=ax] 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(x)=5x
Graph A is f(x)=2x, graph C is f(x)=8x is NOT correct.
So statement 6 is incorrect.
Only statement 1, 2 & 5 are correct.