Question

consider $f(x)=b^x$. which statement(s) are true for $0 < b < 1$? choose four correct answers.
the graph has $x$-intercept 1.
the domain is $x > 0$
the range is $y > 0$.
the range is all real numbers.
the function is always increasing.
the graph has a $y$-intercept of 1.
the domain is all real numbers.
the function is always decreasing.

Explanation:

Step1: Check x-intercept

An x-intercept occurs where $f(x)=0$. For $f(x)=b^x$ with $00$ for all real $x$, so no x-intercept.

Step2: Check domain

Exponential functions $b^x$ accept all real $x$ as inputs, so domain is all real numbers.

Step3: Check range

$b^x$ produces only positive outputs for any real $x$, so range is $y>0$.

Step4: Check y-intercept

Y-intercept is at $x=0$. $f(0)=b^0=1$, so y-intercept is 1.

Step5: Check function trend

For $0

Answer:

• The range is $y > 0$.
• The graph has a y-intercept of 1.
• The domain is all real numbers.
• The function is always decreasing.