Question

Which graph matches the equation ?

Answer 1

I don't see the equation or any graphs — could you paste the equation (and the candidate graphs or descriptions)? I can match them once you do.

Meanwhile, here is a short checklist you can use to match most equations to graphs:

1. Identify the parent function
- Linear: y = mx + b (straight line)
- Quadratic: y = ax^2 + bx + c (parabola)
- Cubic: y = ax^3 + … (S-shaped, odd)
- Absolute value: y = a|x − h| + k (V-shape)
- Square root: y = a√(x − h) + k (starts at h)
- Exponential: y = a·b^x + k (horizontal asymptote y=k)
- Rational: y = (polynomial)/(polynomial) (vertical/horizontal/slant asymptotes)
- Logarithmic: y = a·log(x − h) + k (vertical asymptote x=h)

2. Look for key features
- Intercepts: set x=0 for y-intercept, set y=0 for x-intercepts (solve).
- Asymptotes: rational/exponential/log functions often have them. Vertical where denominator = 0 or domain restriction; horizontal from end behavior.
- Vertex/turning points: quadratics and absolute value have a single vertex.
- Symmetry: even functions (y=f(−x)) are symmetric about y-axis; odd about origin.
- End behavior: as x→±∞, does y→±∞, 0, or a constant? This helps distinguish polynomials, exponentials, rationals.

3. Consider transformations
- y = a·f(b(x − h)) + k: a = vertical stretch/reflection, b = horizontal stretch/compression, (h,k) = shift.

4. Quick checks (use a couple of points)
- Plug in a few x-values to see where the graph should be.

If you post the exact equation and the candidate graphs (or describe them), I’ll match them and explain why.