Question

Which statements accurately describe the function f(x) = 3(16) Superscript three-fourths x? Select three options

Answer 1

Given :   $f(x) = 3(16)^{\frac{3}{4}x } .$   f(x) = 3(16) Superscript three-fourths x  and given 5 statements :

To find :   Select three options  which are correct

Solution:

Given Statements

The initial value is 3   - CORRECT

The domain is x > 0      x can be 0 and - ve

The range is y >0.        CORRECT

The simplified base is 12.

The simplified base is 8.   CORRECT

$f(x) = 3(16)^{\frac{3}{4}x } .$

x = 0

=>f(0) = 3 * 16⁰ = 3 * 1 = 3

hence initial value = 3

x ∈ R  => Domain can be -ve

hence x > 0 is not completely true

$f(x) = 3(16)^{\frac{3}{4}x } .$ > 0    

=> y > 0  

$f(x) = 3(16)^{\frac{3}{4}x } .$

$f(x) = 3(2^4)^{\frac{3}{4}x }$

$f(x) = 3(2)^{3x }$

f(x) = 3 ( 8)ˣ

=> Simplified Base is 8

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