How do you find the x int of f(x)= 4^x (+2)

Question

Pre-calculus

Answer 1

f(x)=4^x+2. To find the x-intercept solve f(x)=0, if possible. So 4^x=-2, which has no solutions because 4^x can only be strictly positive. Therefore there is no x-intercept. Similarly, f(x)=4^x has no x-intercept.

f(x)=4^x+2 has no x-intercept because 4^p>0 for all p, whether positive or negative. As x gets very negative, f(x) gets closer to zero but never reaches zero.

f(x)=4x+2 does have an x-intercept, because 4x+2=0, 4x=-2, when x=-½.

f(x)=x⁴+2 has no x-intercept because all fourth powers are positive so x⁴ can never equal -2.