Question: 1 a)\nf(x) = -2x + 3\n\ng(x) = ?\n\nh = x\n\nk = -1\n\ny = 2x + 3\n\nf\n\ng\n\nh\n\nk\n\nGraph shape: four lines on a coordinate plane. The red line f has equation y = -2x + 3 and slopes downward; the green line h has equation y = x and slopes upward through the origin; the blue line g is an upward-sloping line crossing the y-axis at -2; the black line k is horizontal at y = -1. Position hint: center\nUser: Ist dass richtig und was ist g(x)
1. **Problem statement:** We are given four lines with equations:\n- $f(x) = -2x + 3$ (red line, downward slope)\n- $h(x) = x$ (green line, upward slope through origin)\n- $k(x) = -1$ (black line, horizontal)\n- $g(x) = ?$ (blue line, upward slope crossing y-axis at $-2$)\n\nWe want to find the equation for $g(x)$.\n\n2. **Understanding the problem:** The blue line $g$ is described as an upward-sloping line crossing the y-axis at $-2$. This means the $y$-intercept $b$ of $g(x)$ is $-2$.\n\n3. **General form of a line:** The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.\n\n4. **Finding $g(x)$:** Since $g$ is upward sloping, its slope $m$ is positive. The problem does not give the exact slope, but the user provided $y = 2x + 3$ in the prompt, which is an upward sloping line with slope $2$ and y-intercept $3$. However, the blue line $g$ crosses the y-axis at $-2$, so $b = -2$.\n\n5. **Assuming the slope of $g$ is the same as the given upward slope $2$ (from $y=2x+3$), then:**\n$$g(x) = 2x - 2$$\n\n6. **Summary:**\n- $f(x) = -2x + 3$ (red)\n- $g(x) = 2x - 2$ (blue)\n- $h(x) = x$ (green)\n- $k(x) = -1$ (black)\n\n7. **Answer:** The function $g(x)$ is $$g(x) = 2x - 2$$\n\nThis matches the description of an upward sloping line crossing the y-axis at $-2$.