Answer:
The correct options are 1, 2, 3 and 4.
Step-by-step explanation:
The given function is
[tex]f(x)=2^x[/tex]
The above function is defined for all the values of x.
⇒ Therefore the domain is all real numbers x because the exponent of 2 can be any real number.
⇒ The x is exponent of 2, therefore the x-values increases by 1 unit, the y-value multiplies by 2.
Put x=0, to find the y-intercept.
[tex]f(x)=2^=1[/tex]
⇒The y-intercept is (0, 1).
The value of f(x) is always greater than 0 because powers of 2 are never negative.
[tex]f(x)>0[/tex]
⇒The graph never goes below the x-axis because powers of 2 are never negative.
⇒Therefore the range of the function is all positive real numbers.
Therefore the correct options are 1, 2, 3 and 4.
The True statements about the graph of the function [tex]y =2^x[/tex] are option a), b), c) and d). Refer the below solution for better understanding.
Given :
[tex]y = 2^x[/tex]
Solution :
Domain is all real numbers x because the exponent of 2 can be any real number.
x is exponent of 2, therefore the x-values increases by 1 unit, the y-value multiplies by 2.
At [tex]x=0[/tex],
[tex]y=2^0=1[/tex]
y intercept -- (0 , 1).
y is always greater than zero because power of 2 never be negative.
Graph never goes below the x-axis because powers of 2 are never be negative.
The range of the function is all positive real numbers.
Therefore all the options are correct.
For more information, refer the link given below
https://brainly.com/question/14418346
