Question

question 2
5 pts
which parent function has a y-intercept of 1?

question 3
5 pts
which parent function has no y-intercept?

Explanation:

Question 2

Step1: Recall parent functions and y - intercepts

The y - intercept of a function is the value of the function when \(x = 0\) (provided the function is defined at \(x=0\)). The exponential parent function is \(f(x)=a^{x}\), for the parent exponential function \(f(x) = e^{x}\) or \(f(x)=b^{x}\) with \(b>0,b
eq1\), when \(x = 0\), \(f(0)=b^{0}=1\) (since any non - zero number to the power of 0 is 1). Also, the parent function of the exponential function \(f(x)=a^{x}\) (where \(a>0,a
eq1\)) has a y - intercept of 1. Another example is the parent function of the absolute value function \(y = |x|\) has a y - intercept of 0, the parent linear function \(y=x\) has a y - intercept of 0, the parent quadratic function \(y = x^{2}\) has a y - intercept of 0, but the parent exponential function \(y = a^{x}(a>0,a
eq1)\) has \(y(0)=a^{0}=1\).

Step2: Confirm the function

The parent exponential function \(f(x)=a^{x}\) (e.g., \(f(x)=2^{x}\), \(f(x)=e^{x}\)) has a y - intercept of 1 because when \(x = 0\), \(f(0)=a^{0}=1\) (for \(a>0,a
eq1\)).

Step1: Recall parent functions and their domains

The parent function of the rational function \(f(x)=\frac{1}{x}\) has a domain of \(x
eq0\). The y - intercept occurs at \(x = 0\), but the function \(f(x)=\frac{1}{x}\) is not defined at \(x = 0\). Also, the parent function of the logarithmic function \(y=\log_{a}x\) has a domain of \(x>0\), so \(x = 0\) is not in its domain, but the logarithmic function's y - intercept: when \(x = 0\), \(\log_{a}(0)\) is undefined. However, the parent rational function \(y=\frac{1}{x}\) is a more straightforward example. For \(y=\frac{1}{x}\), to find the y - intercept, we set \(x = 0\), but \(\frac{1}{0}\) is undefined.

Step2: Confirm the function

The parent rational function \(f(x)=\frac{1}{x}\) has no y - intercept because it is not defined at \(x = 0\) (the x - value at which the y - intercept is calculated).

Answer:

The parent exponential function (e.g., \(f(x)=a^{x},a > 0,a
eq1\)) has a y - intercept of 1. A common example is \(f(x)=2^{x}\) (or \(f(x)=e^{x}\) etc.), and when \(x = 0\), \(f(0)=2^{0}=1\) (or \(e^{0}=1\)).

Question 3