Which statements describe the graph of \( y=\sqrt[3]{x-1}+2 \) ? Select three options. The graph has a domain of all real numbers. The graph has a range of \( y \geq 1 \). As \( x \) is increasing, \( y \) is decreasing. The graph has a \( y \)-intercept at \( (0,1) \). The graph has an \( x \)-intercept at \( (-7,0) \).

The graph of \( y=\sqrt[3]{x-1}+2 \) is indeed a fascinating one! For starters, the domain of this function encompasses all real numbers. This is because the cube root function can take any real input, so you can plug in any value of \( x \) without restriction. As for the range, you'll find that it stretches all the way to \( y \geq 2 \), not \( y \geq 1 \). Can you believe it? The function shifts upwards by 2 units due to the \( +2 \). Regarding intercepts, the graph crosses the y-axis at \( (0, \sqrt[3]{-1}+2) = (0, 1) \). So, that part checks out! However, for the x-intercept, \( (-7, 0) \) does not satisfy the equation, so that's a no-go there!