1. Problem: Identify the function for the top-left graph. This is a straight line with positive slope passing through the origin. Formula: $f(x) = mx + b$ Since it passes through origin, $b=0$. Slope $m = \frac{4 - (-3)}{4 - (-3)} = \frac{7}{7} = 1$. Answer: $f(x) = x$ 2. Problem: Identify the function for the top-center graph. This is a parabola opening upward with vertex near (0,1). Formula: $f(x) = a(x - h)^2 + k$ Vertex $(h,k) = (0,1)$. Since it opens upward and passes through (0,1), $a > 0$. Assuming $a=1$ for simplicity. Answer: $f(x) = x^2 + 1$ 3. Problem: Identify the function for the top-right graph. This is a cubic-like curve passing through origin with inflection near origin. Formula: $f(x) = ax^3 + bx^2 + cx + d$ Since passes through origin, $d=0$. Assuming simplest cubic: $f(x) = x^3$ Answer: $f(x) = x^3$ 4. Problem: Identify the function for the middle-left graph. Two branches of hyperbola-like curve approaching 0 at large $x$ and dropping steeply near $x=0$. Formula: $f(x) = \frac{1}{x}$ Answer: $f(x) = \frac{1}{x}$ 5. Problem: Identify the function for the middle-center graph. Square root-like curve starting near (0,0) increasing slowly then faster. Formula: $f(x) = \sqrt{x}$ Answer: $f(x) = \sqrt{x}$ 6. Problem: Identify the function for the middle-right graph. Exponential-like increasing curve starting near $y=0$ for negative $x$ and rising rapidly for positive $x$. Formula: $f(x) = a^x$, $a>1$ Assuming $a=2$. Answer: $f(x) = 2^x$ 7. Problem: Identify the function for the bottom-left graph. Logarithmic-like curve increasing slowly, approaching -3 near $x=-1$. Formula: $f(x) = \log_b(x + c) + d$ Assuming $f(x) = \log(x + 1)$ shifted down 3 units. Answer: $f(x) = \log(x + 1) - 3$ 8. Problem: Identify the function for the bottom-center graph. Waveform oscillating between -2 and 2 on $x \in [-5,5]$. Formula: $f(x) = 2\sin(x)$ Answer: $f(x) = 2\sin(x)$ 9. Problem: Identify the function for the bottom-right graph. Another waveform oscillating between -2 and 2. Formula: $f(x) = 2\cos(x)$ Answer: $f(x) = 2\cos(x)$ 10. Problem: Identify the function for the bottom-left (last row). V-shaped absolute value function crossing origin. Formula: $f(x) = |x|$ Answer: $f(x) = |x|$ 11. Problem: Identify the function for the bottom-center (last row). Step function with filled and open circles at discrete points. This is a floor or stepwise function. Answer: $f(x) = \text{step function defined by given points}$ 12. Problem: Identify the function for the bottom-right (last row). Sigmoid or logistic function increasing from near 0 at $x=-3$ to near 1 at $x=3$. Formula: $f(x) = \frac{1}{1 + e^{-x}}$ Answer: $f(x) = \frac{1}{1 + e^{-x}}$