Let's solve the given equation step by step: ### **Given equation:** \[ y = |x - 3| \] --- ### **Step 1: Find the y-intercept** Set \( x = 0 \): \[ y = |0 - 3| \] \[ y = |-3| \] \[ y = 3 \] **y-intercept:** \((0, 3)\) --- ### **Step 2: Find the x-intercept** Set \( y = 0 \): \[ 0 = |x - 3| \] The absolute value is zero only when the inside is zero: \[ x - 3 = 0 \] \[ x = 3 \] **x-intercept:** \((3, 0)\) --- ### **Step 3: Test for Symmetry** #### **Y-axis symmetry (replace \(x\) with \(-x\)):** \[ y = |(-x) - 3| \] \[ y = |-x - 3| \] This is not the same as the original equation. #### **X-axis symmetry (replace \(y\) with \(-y\)):** \[ -y = |x - 3| \] This is not generally true (since \(|x - 3|\) is always non-negative). #### **Origin symmetry (replace \(x\) with \(-x\), \(y\) with \(-y\)):** \[ -y = |-x - 3| \] This is not the same as the original equation. **Conclusion:** - No y-axis symmetry - No x-axis symmetry - No origin symmetry --- ### **Step 4: Sketch the Graph** The graph of \(y = |x - 3|\) is a V-shape, with the vertex at \(x = 3\), \(y = 0\). It opens upwards. Among the four options, the correct graph is the one with the vertex at (3, 0). --- ### **Step 5: Final Answers** **y-intercept:** (0, 3) **x-intercept:** (3, 0) **Symmetry:** No symmetry **Correct graph:** The bottom right graph (vertex at (3, 0), opening upwards). --- **Summary Table:** | Feature | Value | |-----------------|-----------| | y-intercept | (0, 3) | | x-intercept | (3, 0) | | Symmetry | No symmetry| | Graph | Bottom right | Let me know if you need further explanation!

- **Y-intercept:** (0, 3) - **X-intercept:** (3, 0) - **Symmetry:** No symmetry - **Graph shape:** V-shaped with vertex at (3, 0), opening upwards